A218485 -id:A218485 - cp's OEIS frontend

A218486 Positive numbers differing from next 2 greater squares by squares.

48, 96, 160, 240, 288, 336, 448, 480, 576, 720, 960, 1008, 1344, 1440, 1728, 2016, 2160, 2400, 2640, 2688, 3168, 3360, 3456, 3744, 4320, 4368, 4480, 5040, 5280, 5760, 6336, 6720, 7200, 7488, 8640, 8736, 8800, 9408, 10080, 10560, 10800, 11520, 12096, 12480

Offset: 1

Michel Marcus, Oct 30 2012

nonn

All terms are even. The sequence is infinite. E.g., positive terms of A173121 {48, 288, 960, 2400, 5040, 9408, 16128, 25920, 39600,...} is infinite subsequence of A218486. - Zak Seidov, Nov 26 2013

Another infinite subsequence is {96, 480, 1440, 3360, 6720, 12096, 20160, ...} = 96 *binomial(m,4) = 96*(positive terms in A000332). - Zak Seidov, Nov 26 2013

			48 = 7^2 - 1^2 = 8^2 - 4^2.

Zak Seidov, Table of n, a(n) for n = 1..1000
E. J. Barbeau, Numbers differing from consecutive squares by squares, Canad. Math. Bull. 28(1985), pp. 337-342.

Cf. A173121, A218485, A218487, A218488.

sq2(n) = {for (i=1, n, a = sqrtint(i) + 1; if (issquare(a^2-i) && issquare((a+1)^2-i), print1(i, ", ")););}

A218487 Positive numbers differing from next 3 greater squares by squares.

Original entry on oeis.org

720, 5040, 5760, 10080, 20160, 22176, 28800, 56160, 60480, 100800, 126720, 134640, 151200, 187200, 248976, 262080, 282240, 332640, 428400, 443520, 463680, 665280, 677376, 734400, 763776, 887040, 1108800, 1149120, 1190160, 1235520, 1497600, 1685376, 1718640

Offset: 1

Michel Marcus, Oct 30 2012

nonn

All terms are multiples of 144. - Zak Seidov, Nov 27 2013

			720 = 27^2 - 3^2 = 28^2 - 8^2 = 29^2 - 11^2.

Donovan Johnson, Table of n, a(n) for n = 1..1000
E. J. Barbeau, Numbers differing from consecutive squares by squares, Canad. Math. Bull. 28(1985), pp. 337-342.

Cf. A218485, A218486, A218488.

Select[Range[172*10^4],AllTrue[Sqrt[(Floor[Sqrt[#]]+{1,2,3})^2-#],IntegerQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 18 2021 *)

sq3(n) = {for (i=1, n, a = sqrtint(i) + 1; if (issquare(a^2-i) && issquare((a+1)^2-i) && issquare((a+2)^2-i), print1(i, ", ")););}

A218488 Positive numbers differing from next 4 greater squares by squares.

Original entry on oeis.org

60480, 2851200, 13366080, 42134400, 93139200, 588107520, 684391680, 1210809600, 10534043520, 16817673600, 38694427200, 52143537600, 54939044160, 59580892800, 89555155200, 104432328000, 136734998400, 356676566400, 663924381120, 1100581171200, 1200474475200

Offset: 1

Michel Marcus, Oct 30 2012

nonn

			60480 = 246^2 - 6^2 = 247^2 - 23^2 = 248^2 - 32^2 = 249^2 - 39^2.

Donovan Johnson, Table of n, a(n) for n = 1..84 (terms < 10^18)
E. J. Barbeau, Numbers differing from consecutive squares by squares, Canad. Math. Bull. 28(1985), pp. 337-342.

Cf. A218485, A218486, A218487.

a(9)-a(21) from Donovan Johnson, Oct 31 2012

A342160 Numbers differing from the next greater cube by a cube.

Original entry on oeis.org

0, 7, 19, 26, 37, 56, 63, 98, 117, 124, 152, 189, 208, 215, 218, 279, 316, 335, 342, 387, 448, 485, 504, 511, 513, 604, 665, 702, 721, 728, 784, 875, 936, 973, 992, 999, 1115, 1206, 1267, 1304, 1323, 1330, 1385, 1512, 1603, 1664, 1701, 1720, 1727, 1854, 1981

Offset: 1

Lamine Ngom, Mar 26 2021

Subsequence of A181123.

			37 = 4^3 - 3^3.
117 = 5^3 - 2^3.

Cf. A218485, A181123.

isok(n)={my(t=(sqrtnint(n,3)+1)^3-n); sqrtnint(t,3)^3 == t} \\ Andrew Howroyd, Mar 26 2021

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A218486 Positive numbers differing from next 2 greater squares by squares.

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A218487 Positive numbers differing from next 3 greater squares by squares.

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A218488 Positive numbers differing from next 4 greater squares by squares.

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A342160 Numbers differing from the next greater cube by a cube.

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