The idea was to associate every letter of an alphabet to a number. The number would be converted in base K, where K is the number of letters in the alphabet.
We then want to find palindromic words that, converted in base 10, have also a palindromic number in base 10.
Example:
The word KYRGRYK gives the number 5760110675 in base 10 and BQJ7JQB in base K, using the Spanish alphabet with the letters in alphabetic orders. Though, it does not have a meaning in Spanish. Maybe in other languages.
Finding meaningful words or phrases looks almost impossible. But who knows?
| spanish letters | index | baseK |
|---|---|---|
| _ | 0 | 0 |
| A | 1 | 1 |
| B | 2 | 2 |
| C | 3 | 3 |
| D | 4 | 4 |
| E | 5 | 5 |
| F | 6 | 6 |
| G | 7 | 7 |
| H | 8 | 8 |
| I | 9 | 9 |
| J | 10 | A |
| K | 12 | B |
| L | 11 | C |
| M | 13 | D |
| N | 14 | E |
| Ñ | 15 | F |
| O | 16 | G |
| P | 17 | H |
| Q | 18 | I |
| R | 19 | J |
| S | 20 | K |
| T | 21 | L |
| U | 22 | M |
| V | 23 | N |
| W | 24 | O |
| X | 25 | P |
| Y | 26 | Q |
| Z | 27 | R |
Without being too much optimized and on a random computer such as mine, here are some speed results
| max number | digits | time |
|---|---|---|
| 10^6 = 1_000_000 | 7 | ~2 ms |
| 10^9 = 1_000_000_000 | 10 | ~200 ms |
| 10^12 = 1_000_000_000_000 | 13 | ~2 secs |
| 10^15 = 1_000_000_000_000_000 | 16 | ~2 mins |
| 10^18 = 1_000_000_000_000_000_000 | 19 | ~50 mins |
| Number in base K | Number in base 10 | Word in International Alphabet (Letter in alphabetic order) | Word in International Alphabet (Order by most common letters) | Word in International Alphabet (Letter in alphabetic order with space at the end) |
|---|---|---|---|---|
_ABCDEFGHIJKLMNOPQRSTUVWXYZ |
_EAISNRTOLUDCMPGBVHFQYXJKWZ |
ABCDEFGHIJKLMNOPQRSTUVWXYZ_ |
||
| 0 | 0 | _ | _ | A |
| 1 | 1 | A | E | B |
| 2 | 2 | B | A | C |
| 3 | 3 | C | I | D |
| 4 | 4 | D | S | E |
| 5 | 5 | E | N | F |
| 6 | 6 | F | R | G |
| 7 | 7 | G | T | H |
| 8 | 8 | H | O | I |
| 9 | 9 | I | L | J |
| B | 11 | K | D | L |
| M | 22 | V | X | W |
| 99 | 252 | II | LL | JJ |
| MM | 616 | VV | XX | WW |
| 111 | 757 | AAA | EEE | BBB |
| 141 | 838 | ADA | ESE | BEB |
| 171 | 919 | AGA | ETE | BHB |
| E3E | 10301 | NCN | PIP | ODO |
| HNH | 13031 | QWQ | VJV | RXR |
| LNL | 15951 | UWU | YJY | VXV |
| ODO | 17871 | XMX | KMK | YNY |
| 3993 | 65856 | CIIC | ILLI | DJJD |
| 26N62 | 1197911 | BFWFB | ARJRA | CGXGC |
| 48684 | 2287822 | DHFHD | SOROS | EIGIE |
| 86M68 | 4385834 | HFVFH | ORXRO | IGWGI |
| A858A | 5475745 | JHEHJ | UONOU | KIFIK |
| ABPBA | 5549455 | JKYKJ | UDWDU | KLZLK |
| BLQLB | 6278726 | KUZUK | DYZYD | LV_VL |
| CD8DC | 6639366 | LMHML | CMOMC | MNINM |
| DN9ND | 7368637 | MWIWM | MJLJM | NXJXN |
| E6L6E | 7573757 | NFUFN | PRYRP | OGVGO |
| G848G | 8663668 | PHDHP | BOSOB | QIEIQ |
| GBOBG | 8737378 | PKXKP | BDKDB | QLYLQ |
| HI5IH | 9392939 | QRERQ | VHNHV | RSFSR |
| HLPLH | 9466649 | QUYUQ | VYWYV | RVZVR |
| ID7DI | 9827289 | RMGMR | HMTMH | SNHNS |
| 4IAAI4 | 67166176 | DRJJRD | SHUUHS | ESKKSE |
| EP00PE | 214171412 | NY__YN | PW__WP | OZAAZO |
| 1FDCDF1 | 609808906 | AOMLMOA | EGMCMGE | BPNMNPB |
| 2474742 | 836040638 | BDGDGDB | ASTSTSA | CEHEHEC |
| 5DHAHD5 | 2132882312 | EMQJQME | NMVUVMN | FNRKRNF |
| 6BAGAB6 | 2487997842 | FKJPJKF | RDUBUDR | GLKQKLG |
| DMMJMMD | 5364224635 | MVVSVVM | MXXFXXM | NWWTWWN |
| LJGOGJL | 8417447148 | USPXPSU | YFBKBFY | VTQYQTV |
| NA7N7AN | 9058338509 | WJGWGJW | JUTJTUJ | XKHXHKX |
| 9QPP4PPQ9 | 2823881883282 | IZYYDYYZI | LZWWSWWZL | J_ZZEZZ_J |
| A7IJ8JI7A | 2904768674092 | JGRSHSRGJ | UTHFOFHTU | KHSTITSHK |
| ADMG6GMDA | 2969036309692 | JMVPFPVMJ | UMXBRBXMU | KNWQGQWNK |
| DDPL7LPDD | 3817559557183 | MMYUGUYMM | MMWYTYWMM | NNZVHVZNN |
| E0B474B0E | 3958336338593 | N_KDGDK_N | P_DSTSD_P | OALEHELAO |
| F450O054F | 4280234320824 | ODE_X_EDO | GSN_K_NSG | PEFAYAFEP |
| FK1P6P1KF | 4446399936444 | OTAYFYATO | GQEWRWEQG | PUBZGZBUP |
| G04D0D40G | 4520609060254 | P_DM_MD_P | B_SM_MS_B | QAENANEAQ |
| GJLF4FLJG | 4725972795274 | PSUODOUSP | BFYGSGYFB | QTVPEPVTQ |
| H0E989E0H | 4806859586084 | Q_NIHIN_Q | V_PLOLP_V | RAOJIJOAR |
| HNQJNJQNH | 5052248422505 | QWZSWSZWQ | VJZFJFZJV | RX_TXT_XR |
| IAC2N2CAI | 5193025203915 | RJLBWBLJR | HUCAJACUH | SKMCXCMKS |
| KCE030ECK | 5779540459775 | TLN_C_NLT | QCP_I_PCQ | UMOADAOMU |
| L7PPEPP7L | 6014294924106 | UGYYNYYGU | YTWWPWWTY | VHZZOZZHV |
| LAF7O7FAL | 6041548451406 | UJOGXGOJU | YUGTKTGUY | VKPHYHPKV |
| 2KNIH1HINK2 | 570984989489075 | BTWRQAQRWTB | AQJHVEVHJQA | CUXSRBRSXUC |
| 403Q464Q304 | 824685424586428 | D_CZDFDZC_D | S_IZSRSZI_S | EAD_EGE_DAE |
| 46CN9I9NC64 | 872951606159278 | DFLWIRIWLFD | SRCJLHLJCRS | EGMXJSJXMGE |
| 4I8CJ5JC8I4 | 963217686712369 | DRHLSESLHRD | SHOCFNFCOHS | ESIMTFTMISE |
| 4LC28982CL4 | 987115383511789 | DULBHIHBLUD | SYCAOLOACYS | EVMCIJICMVE |
| 659CHHHC956 | 1276149009416721 | FEILQQQLIEF | RNLCVVVCLNR | GFJMRRRMJFG |
| C87JG8GJ78C | 2533880440883352 | LHGSPHPSGHL | COTFBOBFTOC | MIHTQIQTHIM |
| I8PG050GP8I | 3774273333724773 | RHYP_E_PYHR | HOWB_N_BWOH | SIZQAFAQZIS |
| BA44ACCA44AB | 63240319091304236 | KJDDJLLJDDJK | DUSSUCCUSSUD | LKEEKMMKEEKL |
| 1Q60LFAFL06Q1 | 295871648846178592 | AZF_UOJOU_FZA | EZR_YGUGY_RZE | B_GAVPKPVAG_B |
| 3GDCEIDIECDG3 | 542001114445237365 | CPMLNRMRNLMPC | IBMCPHMHPCMBI | DQNMOSNSOMNQD |
| 507CB4B4BC705 | 752009074470900257 | E_GLKDKDKLG_E | N_TCDSDSDCT_N | FAHMLELELMHAF |
| 6A42DMLMD24A6 | 957001143341100759 | FJDBMVUVMBDJF | RUSAMXYXMASUR | GKECNWVWNCEKG |
| Number in base K | Number in base 10 | Word in Spanish Alphabet (Letter in alphabetic order) | Word in Spanish Alphabet (Vowel in even position) | Word in Spanish Alphabet (Vowel in odd position) | Word in Spanish Alphabet (Order by most common letters) | Word in Spanish Alphabet (Vowels first) | Word in Spanish Alphabet (Order random) | Word in Spanish Alphabet (Letter in alphabetic order with space at the end) |
|---|---|---|---|---|---|---|---|---|
_ABCDEFGHIJKLMNÑOPQRSTUVWXYZ |
_BACDFEGHJIKLMNÑOPQRSTUVWXYZ |
_ABCDEFGHIJKLMNOÑPQRSUTVWYXZ |
_EAOSRNIDLCTUMPBGVYQHFZJÑXKW |
_EAOIUNSDLCTRMPBGVYQHFZJÑXKW |
_EAFIUNSDLCTRMPBGJYQHOZVÑXKW |
ABCDEFGHIJKLMNÑOPQRSTUVWXYZ_ |
||
| 0 | 0 | _ | _ | _ | _ | _ | _ | A |
| 1 | 1 | A | B | A | E | E | E | B |
| 2 | 2 | B | A | B | A | A | A | C |
| 3 | 3 | C | C | C | O | O | F | D |
| 4 | 4 | D | D | D | S | I | I | E |
| 5 | 5 | E | F | E | R | U | U | F |
| 6 | 6 | F | E | F | N | N | N | G |
| 7 | 7 | G | G | G | I | S | S | H |
| 8 | 8 | H | H | H | D | D | D | I |
| 9 | 9 | I | J | I | L | L | L | J |
| B | 11 | K | K | K | T | T | T | L |
| M | 22 | U | U | T | Z | Z | Z | V |
| 88 | 232 | HH | HH | HH | DD | DD | DD | II |
| GG | 464 | OO | OO | ÑÑ | GG | GG | GG | PP |
| OO | 696 | WW | WW | WW | ÑÑ | ÑÑ | ÑÑ | XX |
| 7A7 | 5775 | GJG | GIG | GJG | ICI | SCS | SCS | HKH |
| 828 | 6336 | HBH | HAH | HBH | DAD | DAD | DAD | ICI |
| D7D | 10401 | MGM | MGM | MGM | MIM | MSM | MSM | NHN |
| JCJ | 15251 | RLR | RLR | RLR | QUQ | QRQ | QRQ | SMS |
| LHL | 16961 | TPT | TPT | UPU | FVF | FVF | OJO | UQU |
| QEQ | 20802 | YNY | YNY | XNX | KPK | KPK | KPK | ZÑZ |
| 4NBN4 | 2972792 | DVKVD | DVKVD | DVKVD | SJTJS | IJTJI | IVTVI | EWLWE |
| 97D79 | 5695965 | IGMGI | JGMGJ | IGMGI | LIMIL | LSMSL | LSMSL | JHNHJ |
| A3O3A | 6231326 | JCWCJ | ICWCI | JCWCJ | COÑOC | COÑOC | CFÑFC | KDXDK |
| AKJKA | 6601066 | JSRSJ | ISRSI | JSRSJ | CHQHC | CHQHC | CHQHC | KTSTK |
| BB0BB | 7003007 | KK_KK | KK_KK | KK_KK | TT_TT | TT_TT | TT_TT | LLALL |
| E8A8E | 8788878 | NHJHN | NHIHN | NHJHN | PDCDP | PDCDP | PDCDP | ÑIKIÑ |
| F4L4F | 9324239 | ÑDTDÑ | ÑDTDÑ | ODUDO | BSFSB | BIFIB | BIOIB | OEUEO |
| H282H | 10499401 | PBHBP | PAHAP | PBHBP | VADAV | VADAV | JADAJ | QCICQ |
| 9A00A9 | 161040161 | IJ__JI | JI__IJ | IJ__JI | LC__CL | LC__CL | LC__CL | JKAAKJ |
| ONQQNO | 427777724 | WVYYVW | WVYYVW | WVXXVW | ÑJKKJÑ | ÑJKKJÑ | ÑVKKVÑ | XWZZWX |
| 112C211 | 500595005 | AABLBAA | BBALABB | AABLBAA | EEAUAEE | EEARAEE | EEARAEE | BBCMCBB |
| 1D9R9D1 | 711757117 | AMIZIMA | BMJZJMB | AMIZIMA | EMLWLME | EMLWLME | EMLWLME | BNJ_JNB |
| 1FILIF1 | 751585157 | AÑQTQÑA | BÑQTQÑB | AOQUQOA | EBYFYBE | EBYFYBE | EBYOYBE | BORUROB |
| 1GR3RG1 | 773939377 | AOZCZOA | BOZCZOB | AÑZCZÑA | EGWOWGE | EGWOWGE | EGWFWGE | BP_D_PB |
| 1OF0FO1 | 904171409 | AWÑ_ÑWA | BWÑ_ÑWB | AWO_OWA | EÑB_BÑE | EÑB_BÑE | EÑB_BÑE | BXOAOXB |
| 1R0Q0R1 | 947141749 | AZ_Y_ZA | BZ_Y_ZB | AZ_X_ZA | EW_K_WE | EW_K_WE | EW_K_WE | B_AZA_B |
| 35B8B53 | 1538668351 | CEKHKEC | CFKHKFC | CEKHKEC | ORTDTRO | OUTDTUO | FUTDTUF | DFLILFD |
| BQJ7JQB | 5760110675 | KYRGRYK | KYRGRYK | KXRGRXK | TKQIQKT | TKQSQKT | TKQSQKT | LZSHSZL |
| CMM7MMC | 6175005716 | LUUGUUL | LUUGUUL | LTTGTTL | UZZIZZU | RZZSZZR | RZZSZZR | MVVHVVM |
| F41E14F | 7298118927 | ÑDANADÑ | ÑDBNBDÑ | ODANADO | BSEPESB | BIEPEIB | BIEPEIB | OEBÑBEO |
| LOR6ROL | 10549494501 | TWZFZWT | TWZEZWT | UWZFZWU | FÑWNWÑF | FÑWNWÑF | OÑWNWÑO | UX_G_XU |
| N96L69N | 11242524211 | VIFTFIV | VJETEJV | VIFUFIV | JLNFNLJ | JLNFNLJ | VLNONLV | WJGUGJW |
| RD8E8DR | 13240004231 | ZMHNHMZ | ZMHNHMZ | ZMHNHMZ | WMDPDMW | WMDPDMW | WMDPDMW | _NIÑIN_ |
| RKCNCKR | 13363136331 | ZSLVLSZ | ZSLVLSZ | ZSLVLSZ | WHUJUHW | WHRJRHW | WHRVRHW | _TMWMT_ |
| 5O5DD5O5 | 79124342197 | EWEMMEWE | FWFMMFWF | EWEMMEWE | RÑRMMRÑR | UÑUMMUÑU | UÑUMMUÑU | FXFNNFXF |
| 6H7EE7H6 | 89279097298 | FPGNNGPF | EPGNNGPE | FPGNNGPF | NVIPPIVN | NVSPPSVN | NJSPPSJN | GQHÑÑHQG |
| KD5HH5DK | 276220022672 | SMEPPEMS | SMFPPFMS | SMEPPEMS | HMRVVRMH | HMUVVUMH | HMUJJUMH | TNFQQFNT |
| 11A414A11 | 396183381693 | AAJDADJAA | BBIDBDIBB | AAJDADJAA | EECSESCEE | EECIEICEE | EECIEICEE | BBKEBEKBB |
| 1Q5AKA5Q1 | 731212212137 | AYEJSJEYA | BYFISIFYB | AXEJSJEXA | EKRCHCRKE | EKUCHCUKE | EKUCHCUKE | BZFKTKFZB |
| 6RA555AR6 | 2636029206362 | FZJEEEJZF | EZIFFFIZE | FZJEEEJZF | NWCRRRCWN | NWCUUUCWN | NWCUUUCWN | G_KFFFK_G |
| 9EI4G4IE9 | 3597871787953 | INQDODQNI | JNQDODQNJ | INQDÑDQNI | LPYSGSYPL | LPYIGIYPL | LPYIGIYPL | JÑREPERÑJ |
| APBDBDBPA | 4120874780214 | JXKMKMKXJ | IXKMKMKXI | JYKMKMKYJ | CXTMTMTXC | CXTMTMTXC | CXTMTMTXC | KYLNLNLYK |
| CC8J1J8CC | 4699722279964 | LLHRARHLL | LLHRBRHLL | LLHRARHLL | UUDQEQDUU | RRDQEQDRR | RRDQEQDRR | MMISBSIMM |
| F910C019F | 5788955598875 | ÑIA_L_AIÑ | ÑJB_L_BJÑ | OIA_L_AIO | BLE_U_ELB | BLE_R_ELB | BLE_R_ELB | OJBAMABJO |
| GP62L26PG | 6385093905836 | OXFBTBFXO | OXEATAEXO | ÑYFBUBFYÑ | GXNAFANXG | GXNAFANXG | GXNAOANXG | PYGCUCGYP |
| M1EHRHE1M | 8332192912338 | UANPZPNAU | UBNPZPNBU | TANPZPNAT | ZEPVWVPEZ | ZEPVWVPEZ | ZEPJWJPEZ | VBÑQ_QÑBV |
| M1RAIAR1M | 8338331338338 | UAZJQJZAU | UBZIQIZBU | TAZJQJZAT | ZEWCYCWEZ | ZEWCYCWEZ | ZEWCYCWEZ | VB_KRK_BV |
| PICF3FCIP | 9693965693969 | XQLÑCÑLQX | XQLÑCÑLQX | YQLOCOLQY | XYUBOBUYX | XYRBOBRYX | XYRBFBRYX | YRMODOMRY |
| 53APRRPA35 | 54173144137145 | ECJXZZXJCE | FCIXZZXICF | ECJYZZYJCE | ROCXWWXCOR | UOCXWWXCOU | UFCXWWXCFU | FDKY__YKDF |
| 124HGGGH421 | 319102262201913 | ABDPOOOPDBA | BADPOOOPDAB | ABDPÑÑÑPDBA | EASVGGGVSAE | EAIVGGGVIAE | EAIJGGGJIAE | BCEQPPPQECB |
| 1LIJFQFJIL1 | 525408828804525 | ATQRÑYÑRQTA | BTQRÑYÑRQTB | AUQROXORQUA | EFYQBKBQYFE | EFYQBKBQYFE | EOYQBKBQYOE | BURSOZOSRUB |
| 1NOG363GON1 | 548785939587845 | AVWOCFCOWVA | BVWOCECOWVB | AVWÑCFCÑWVA | EJÑGONOGÑJE | EJÑGONOGÑJE | EVÑGFNFGÑVE | BWXPDGDPXWB |
| 23ED5H5DE32 | 629596242695926 | BCNMEPEMNCB | ACNMFPFMNCA | BCNMEPEMNCB | AOPMRVRMPOA | AOPMUVUMPOA | AFPMUJUMPFA | CDÑNFQFNÑDC |
| 2OA5EDE5AO2 | 850128939821058 | BWJENMNEJWB | AWIFNMNFIWA | BWJENMNEJWB | AÑCRPMPRCÑA | AÑCUPMPUCÑA | AÑCUPMPUCÑA | CXKFÑNÑFKXC |
| 32MOQRQOM23 | 918395696593819 | CBUWYZYWUBC | CAUWYZYWUAC | CBTWXZXWTBC | OAZÑKWKÑZAO | OAZÑKWKÑZAO | FAZÑKWKÑZAF | DCVXZ_ZXVCD |
| HK82EEE28KH | 5249970550799425 | PSHBNNNBHSP | PSHANNNAHSP | PSHBNNNBHSP | VHDAPPPADHV | VHDAPPPADHV | JHDAPPPADHJ | QTICÑÑÑCITQ |
| 2C6E7117E6C2 | 20210235053201202 | BLFNGAAGNFLB | ALENGBBGNELA | BLFNGAAGNFLB | AUNPIEEIPNUA | ARNPSEESPNRA | ARNPSEESPNRA | CMGÑHBBHÑGMC |
| 19PG2HNH2GP91 | 314435021120534413 | AIXOBPVPBOXIA | BJXOAPVPAOXJB | AIYÑBPVPBÑYIA | ELXGAVJVAGXLE | ELXGAVJVAGXLE | ELXGAJVJAGXLE | BJYPCQWQCPYJB |
To improve the search, it needs to improve the way we find palindromic numbers. It's already good, but not perfect.
Also, we can try to optimize even better the computation accross threads.