OFFSET
0,6
COMMENTS
If such an m>0 exists, this proves that n is not in A051213, i.e., not of the form 2^x-y^2. On the other hand, if there are integers x, y such that n=2^x-y^2, then we know that a(n)=0.
a(519) > 20000 if it is nonzero.
It remains to show whether "a(n)=0" is equivalent to "n is in A051213". For example, one can show that 519 is not in A051213, but we don't know a(519) yet. - M. F. Hasler, Oct 23 2014
LINKS
M. F. Hasler, Table of n, a(n) for n = 0..518
EXAMPLE
See A200507 for motivation and examples.
PROG
(PARI) A200522(n, b=2, p=3)={ my( x=0, qr, bx, seen ); for( m=3, 9e9, while( x^p < m, issquare(b^x-n) & return(0); x++); qr=vecsort(vector(m, y, y^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