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

1,1

Comments

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

Links

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.

Example

8 = 3^2 - 1^2.

Mathematica

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

Prog

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

Crossrefs

Cf. A060300, A218486, A218487, A218488.

Sequence in context: A287380 A339389 A348236 * A310029 A310030 A045716

Adjacent sequences: A218482 A218483 A218484 * A218486 A218487 A218488

Keyword

nonn

Author

Michel Marcus, Oct 30 2012

Status

approved