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A200518 Least m>0 such that n = y^2-8^x (mod m) has no solution, or 0 if no such m exists. 1
0, 0, 4, 0, 7, 7, 4, 9, 0, 7, 4, 7, 7, 8, 4, 0, 7, 0, 4, 7, 32, 8, 4, 7, 0, 7, 4, 16, 0, 8, 4, 9, 7, 7, 4, 0, 0, 7, 4, 7, 7, 0, 4, 9, 7, 8, 4, 7, 0, 9, 4, 7, 9, 7, 4, 12, 0, 0, 4, 16, 7, 7, 4, 0, 0, 7, 4, 7, 7, 8, 4, 16, 7, 0, 4, 7, 9, 8, 4, 7, 0, 7, 4, 32 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

If a(n)>0, this proves that n cannot be a member of A051210, i.e., cannot be written as y^2-8^x. To prove that an integer n is in A051210, it is sufficient to find integers x,y such that y^2-8^x=n. In that case, a(n)=0.

LINKS

M. F. Hasler, Table of n, a(n) for n = 0..1000

EXAMPLE

See A200512 for motivation and detailed examples.

PROG

(PARI) A200518(n, b=8, 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

Cf. A051204-A051221, A200505-A200520.

Sequence in context: A170990 A013666 A196533 * A016682 A198741 A298617

Adjacent sequences:  A200515 A200516 A200517 * A200519 A200520 A200521

KEYWORD

nonn

AUTHOR

M. F. Hasler, Nov 18 2011

STATUS

approved

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Last modified May 13 00:11 EDT 2021. Contains 343829 sequences. (Running on oeis4.)