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A200520 Least m>0 such that n = y^2 - 10^x (mod m) has no solution, or 0 if no such m exists. 13
0, 3, 5, 0, 3, 9, 0, 3, 0, 11, 3, 9, 5, 3, 9, 0, 3, 5, 11, 3, 9, 0, 3, 9, 0, 3, 0, 5, 3, 9, 16, 3, 5, 20, 3, 0, 1001, 3, 9, 0, 3, 9, 5, 3, 0, 56, 3, 5, 0, 3, 9, 11, 3, 11, 0, 3, 9, 5, 3, 9, 112, 3, 5, 0, 3, 9, 16, 3, 9, 0, 3, 0, 5, 3, 9, 11, 3, 5, 16, 3, 0, 3367 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

To prove that an integer n is in A051212, it is sufficient to find integers x,y such that y^2 - 10^x = n. In that case, a(n)=0. To prove that n is *not* in A051212, it is sufficient to find a modulus m for which the (finite) set of all possible values of 10^x and y^2 allows us to deduce that y^2 - 10^x can never equal n. The present sequence lists the smallest such m>0, if it exists.

LINKS

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

EXAMPLE

See A200512 for motivation and detailed examples.

PROG

(PARI) A200520(n, b=10, 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-A200524.

Sequence in context: A153099 A102575 A309091 * A224933 A307209 A243967

Adjacent sequences:  A200517 A200518 A200519 * A200521 A200522 A200523

KEYWORD

nonn

AUTHOR

M. F. Hasler, Nov 18 2011

STATUS

approved

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Last modified October 19 16:17 EDT 2019. Contains 328223 sequences. (Running on oeis4.)