

A200518


Least m>0 such that n = y^28^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
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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^28^x. To prove that an integer n is in A051210, it is sufficient to find integers x,y such that y^28^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^2n)%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. A051204A051221, A200505A200520.
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



