A200440 -id:A200440 - cp's OEIS frontend

A051217 Nonnegative numbers of the form 6^x - y^2.

0, 1, 2, 5, 6, 11, 20, 27, 32, 35, 36, 47, 71, 72, 95, 116, 135, 140, 152, 167, 180, 191, 200, 207, 212, 215, 216, 272, 335, 380, 396, 431, 455, 512, 551, 567, 620, 671, 720, 767, 812, 855, 860, 887, 896, 935, 972, 1007, 1040, 1052, 1071, 1100, 1127, 1152

Offset: 1

David W. Wilson

nonn

No integers congruent to {3,4,8,9} mod 10. - Zak Seidov, Nov 14 2011

If k is not in this sequence, then A200440 gives the least modulus which proves that there cannot be a solution to k = 6^x - y^2. - M. F. Hasler, Nov 18 2011

Hugo Pfoertner, Table of n, a(n) for n = 1..513

Cf. A201122.

max = 10^5; Clear[f]; f[m_] := f[m] = Select[Table[6^x - y^2, {x, 0, m}, {y, 0, Ceiling[6^(x/2)]}] // Flatten // Union, 0 <= # <= max &]; f[1]; f[m = 2]; While[f[m] != f[m - 1], m++]; Print["m = ", m]; A051217 = f[m] (* Jean-François Alcover, May 13 2017 *)

is_A051217(n) = !A200440(n)  \\ M. F. Hasler, Nov 18 2011

A201122 Differences between odd powers of 6 and the next smaller square.

Original entry on oeis.org

2, 20, 32, 95, 3420, 8847, 89927, 494576, 1347932, 48525552, 265807127, 682379927, 3237653360, 52571448911, 356954431580, 1333226567615, 6534477744687, 69394484050880, 10500704463815, 378025360697340, 13608912985104240, 60046182811381232, 227226500274052935, 442409686123219952, 15926748700435918272

Offset: 1

Hugo Pfoertner, Nov 27 2011

nonn

			a(1)=6^1-2^2=2, a(2)=6^3-14^2=216-196=20, a(3)=6^5-88^2=7776-7744=32

Hugo Pfoertner, Table of n, a(n) for n = 1..500

Cf. A051217, A200440, A200506

#-Floor[Sqrt[#]]^2&/@(6^Range[1,51,2]) (* Harvey P. Dale, Aug 12 2012 *)

a(n)=6^(2*n-1) - floor(sqrt(6^(2*n-1)))^2

cp's OEIS Frontend

A051217 Nonnegative numbers of the form 6^x - y^2.

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