OFFSET
0,4
COMMENTS
If such an m>0 exists, this proves that n is not in A051217, i.e., not of the form 6^x-y^2. On the other hand, if there are integers x, y such that n=6^x-y^2, then we know that a(n)=0.
LINKS
M. F. Hasler, Table of n, a(n) for n = 0..1000
FORMULA
a(3+5k)=a(4+5k)=5, a(10+35k)=a(17+35k)=a(31+35k)=7 for all k>=0.
a(n)=9 for n=7, 16, 22, 70, 76 and 85 (mod 90).
EXAMPLE
See A200507.
PROG
(PARI) A200506(n, b=6, p=3)={ my( x=0, qr, bx, seen ); for( m=2, 9e9, while( x^p < m, issquare(b^x-n) & return(0); x++); qr=vecsort(vector(m, i, i^2+n)%m, , 8); seen=0; bx=1; until( bittest(seen+=1<<bx, bx=bx*b%m), for(i=1, #qr, qr[i]<bx & next; qr[i]>bx & break; next(3))); return(m))}
CROSSREFS
KEYWORD
nonn
AUTHOR
M. F. Hasler, Nov 18 2011
STATUS
approved