The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A248746

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A248746

a(n) is the index k of the greatest prime divisor A002313(k) of n^2 + 1.
(history; published version)

#10 by N. J. A. Sloane at Sat Feb 06 21:52:52 EST 2021

STATUS

editing

approved

#9 by N. J. A. Sloane at Sat Feb 06 21:52:44 EST 2021

COMMENTS

A014442 (greatest prime divisor of n^2+1).

A002313 (primes congruent to 1 or 2 modulo 4).

CROSSREFS

Cf. A002313, A002522, A014442 (greatest prime divisor of n^2+1), A002313 (primes congruent to 1 or 2 modulo 4).

Cf. also A002522.

STATUS

proposed

editing

Discussion

Sat Feb 06

21:52

N. J. A. Sloane: done

#8 by Jon E. Schoenfield at Sat Feb 06 15:00:42 EST 2021

STATUS

editing

proposed

#7 by Jon E. Schoenfield at Sat Feb 06 14:59:54 EST 2021

NAME

a(n) is the index k of the greatest prime divisor A002313(k) of n^2 + 1.

COMMENTS

a(n) is the number k such that A002313(k) = A014442(n).

STATUS

approved

editing

Discussion

Sat Feb 06

15:00

Jon E. Schoenfield: Should the 2nd and 3rd lines in the Comments be crossrefs?

#6 by Peter Luschny at Wed Nov 05 13:03:03 EST 2014

STATUS

reviewed

approved

#5 by Wouter Meeussen at Wed Oct 29 13:48:05 EDT 2014

STATUS

proposed

reviewed

#4 by Michel Lagneau at Mon Oct 13 07:06:08 EDT 2014

STATUS

editing

proposed

Discussion

Wed Oct 29

13:48

Wouter Meeussen: Data set shown checks out ok.

#3 by Michel Lagneau at Mon Oct 13 07:03:54 EDT 2014

LINKS

Michel Lagneau, <a href="/A248746/b248746.txt">Table of n, a(n) for n = 1..5000</a>

Discussion

Mon Oct 13

07:05

Michel Lagneau: In order to obtain 5000 successive correct values in the b-file, T:=array(1..1500000) and nn:=10^7 are sufficient in the Maple program.

#2 by Michel Lagneau at Mon Oct 13 07:02:06 EDT 2014

NAME

allocated for Michel Lagneaua(n) is the index k of the greatest prime divisor A002313(k) of n^2+1.

DATA

1, 2, 2, 4, 3, 6, 2, 3, 7, 13, 9, 5, 4, 22, 15, 26, 5, 3, 20, 39, 4, 12, 8, 51, 31, 60, 10, 18, 41, 8, 6, 7, 14, 11, 54, 105, 16, 4, 65, 121, 5, 35, 6, 17, 83, 10, 4, 45, 97, 9, 106, 48, 29, 209, 11, 221, 3, 59, 133, 28, 138, 66, 38, 25, 155, 294, 43, 6, 174, 5

OFFSET

1,2

COMMENTS

a(n) is the number k such that A002313(k)= A014442(n).

A014442 (greatest prime divisor of n^2+1).

A002313 (primes congruent to 1 or 2 modulo 4).

EXAMPLE

a(5)=3 because A002313(3)=13 and 5^2+1 = 2*13 with A002313(3)= A014442(5).

MAPLE

with(numtheory):T:=array(1..50000):T[1]:=2:kk:=1:nn:=10^5:

for i from 1 to nn do:

p:=4*i+1:

if type(p, prime)=true

then

kk:=kk+1:T[kk]:=p:

else

fi:

od:

for k from 1 to 5000 do:ii:=0:

y:=factorset(k^2+1):n2:=nops(y):t:=y[n2]:

for l from 1 to kk while(ii=0)do :

if t=T[l]

then

printf(`%d, `, l):

else

fi:

od:

CROSSREFS

Cf. A002313, A002522, A014442.

KEYWORD

allocated

nonn

AUTHOR

Michel Lagneau, Oct 13 2014

STATUS

approved

editing

#1 by Michel Lagneau at Mon Oct 13 07:02:06 EDT 2014

NAME

allocated for Michel Lagneau

KEYWORD

allocated

STATUS

approved