A218488 -id:A218488 - cp's OEIS frontend

A218485 Positive numbers differing from next greater square by a square.

3, 5, 8, 12, 15, 16, 21, 24, 27, 32, 35, 40, 45, 48, 55, 60, 63, 65, 72, 77, 80, 84, 91, 96, 99, 105, 112, 117, 120, 128, 135, 140, 143, 144, 153, 160, 165, 168, 171, 180, 187, 192, 195, 200, 209, 216, 221, 224, 231, 240, 247, 252, 255, 264, 273, 280, 285

Offset: 1

Michel Marcus, Oct 30 2012

nonn

Square terms in the sequence are 16, 144, 576, 1600, 3600, 7056, ..., that is, A060300 ((2n(n+1))^2) except 0. And their indices, ind(n), are: 6, 34, 100, 220, 410, 686, ..., that is, ind(n) = 2*A132124(.). - Michel Marcus, suggested by Zak Seidov, Nov 26 2013

			8 = 3^2 - 1^2.

Zak Seidov, Table of n, a(n) for n = 1..1515 (all terms up to 20000)
E. J. Barbeau, Numbers differing from consecutive squares by squares, Canad. Math. Bull. 28(1985), pp. 337-342.

Cf. A060300, A218486, A218487, A218488.

Select[Range[300],IntegerQ[Sqrt[(1+Floor[Sqrt[#]])^2-#]]&] (* Zak Seidov, Nov 26 2013 *)

sq1(n) = {for (i=1, n, a = sqrtint(i) + 1; if (issquare(a^2-i), print1(i, ", ")););}

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

Original entry on oeis.org

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, ", ")););}

cp's OEIS Frontend

A218485 Positive numbers differing from next greater square by a square.

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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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Mathematica

PARI