A051219 -id:A051219 - cp's OEIS frontend

A051220 Numbers of the form 9^x-y^2 >= 0.

0, 1, 5, 8, 9, 17, 32, 45, 53, 56, 65, 72, 77, 80, 81, 104, 153, 161, 200, 245, 288, 320, 329, 368, 405, 440, 473, 477, 485, 504, 533, 560, 585, 608, 629, 632, 648, 665, 680, 693, 704, 713, 720, 725, 728, 729, 785, 936, 968, 1085, 1232, 1377, 1449, 1457, 1520

Offset: 1

David W. Wilson

nonn

max = 2000; Clear[f]; f[m_] := f[m] = Select[Table[9^x - y^2, {x, 0, m}, {y, 0, Ceiling[9^(x/2)]}] // Flatten // Union, 0 <= # <= max &]; f[1]; f[m = 2]; While[f[m] != f[m - 1], m++]; Print["m = ", m]; A051219 = f[m] (* Jean-François Alcover, May 14 2017 *)

A200508 Least m>0 such that n = 8^x-y^2 (mod m) has no solution, or 0 if no such m exists.

Original entry on oeis.org

0, 0, 4, 7, 0, 7, 4, 0, 0, 7, 4, 8, 7, 20, 4, 0, 7, 7, 4, 7, 9, 16, 4, 7, 7, 16, 4, 8, 0, 9, 4, 7, 9, 7, 4, 8, 48, 7, 4, 0, 7, 9, 4, 8, 7, 7, 4, 7, 0, 20, 4, 7, 7, 12, 4, 0, 9, 16, 4, 7, 0, 7, 4, 0, 0, 7, 4, 8, 7, 16, 4, 0, 7, 7, 4, 7, 32, 9, 4, 7, 7, 44, 4

Offset: 0

M. F. Hasler, Nov 18 2011

nonn

If such an m>0 exists, this proves that n is not in A051219, i.e., not of the form 8^x-y^2. On the other hand, if n is in A051219, i.e., there are integers x, y such that n=8^x-y^2, then we know that a(n)=0.

			See A200507.

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

Cf. A051204-A051221, A200505-A200524.

A200508(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,i,i^2+n)%m,,8); seen=0; bx=1; until( bittest(seen+=1<bx & break; next(3))); return(m))}

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A051220 Numbers of the form 9^x-y^2 >= 0.

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A200508 Least m>0 such that n = 8^x-y^2 (mod m) has no solution, or 0 if no such m exists.

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