A218487 -id:A218487 - 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, ", ")););}

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

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

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

Views

Author

Keywords

Examples

Links

Crossrefs

Extensions