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 A051213 Numbers of the form 2^x-y^2 >= 0. 6
 0, 1, 2, 3, 4, 7, 8, 12, 15, 16, 23, 28, 31, 32, 39, 47, 48, 55, 60, 63, 64, 71, 79, 87, 92, 103, 112, 119, 124, 127, 128, 135, 151, 156, 175, 183, 188, 192, 199, 207, 220, 223, 231, 240, 247, 252, 255, 256, 271, 284, 287, 295, 316, 343, 348, 367, 368, 375, 391, 399, 412, 431, 448 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Is 519 in this sequence? Then this is the value of a(73), else it is 527, after which the sequence goes on with 540, 583, 604, 615, 623, 624,... - M. F. Hasler, Oct 09 2014 From R. J. Mathar, Oct 21 2014: (Start) 519 is not in the sequence. [Proof: Consider 2^x-519=y^2 and both sides modulo 3. Then 2^x-519 = 1,2,1,2.... (mod 3) for x>=0 and y^2=0,1,1,0,1,1,... (mod 3) for y>=0. For moduli to match (i.e, both 1), x must be even. Then 2^x is the square of the integer y=2^(x/2). (Note that this reference does not work in integers if x is odd). The next smaller perfect square is (y-1)^2 = (2^(x/2)-1)^2 = 2^x-2^(1+x/2)+1 . This must be >=2^x-519 to have a solution, so -2^(1+x/2)+1 >= -519 implies 2^(1+x/2)-1 <= 519, which implies 1+x/2 <= 9.02 and x<=16. One can check numerically that the range 0<=x<=16 do not form perfect squares 2^x-519.] (End) LINKS M. F. Hasler, Table of n, a(n) for n = 1..72 J. Cohn, The diophantine equation x^2+C=y^n, Acta Arithm. 65 (4) (1993) 367-381 Fadwa S. Abu Muriefah, Yann Bugeaud, The diophantine equation x^2+c=y^n: a brief overview, Rev. Colomb. Matem. 40 (1) (2006) 31-37 MATHEMATICA max = 1000; Clear[f]; f[m_] := f[m] = Select[Table[2^x - y^2, {x, 0, m}, {y, 0, Ceiling[2^(x/2)]}] // Flatten // Union, 0 <= # <= max &]; f; f[m = 2]; While[f[m] != f[m - 1], m++]; Print["m = ", m]; A051213 = f[m] (* Jean-François Alcover, May 13 2017 *) PROG (PARI) is_A051213(n)=!A200522(n) \\ M. F. Hasler, Oct 09 2014 CROSSREFS Cf. A201125. Sequence in context: A186243 A073882 A015840 * A211659 A301806 A066847 Adjacent sequences:  A051210 A051211 A051212 * A051214 A051215 A051216 KEYWORD nonn AUTHOR EXTENSIONS More terms from M. F. Hasler, Oct 09 2014 STATUS approved

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Last modified January 26 08:18 EST 2020. Contains 331278 sequences. (Running on oeis4.)