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A218485 Positive numbers differing from next greater square by a square. 5
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 (list; graph; refs; listen; history; text; internal format)
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 - A218488.

Sequence in context: A285953 A287380 A339389 * A310029 A310030 A045716

Adjacent sequences:  A218482 A218483 A218484 * A218486 A218487 A218488

KEYWORD

nonn

AUTHOR

Michel Marcus, Oct 30 2012

STATUS

approved

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Last modified September 23 20:42 EDT 2021. Contains 347617 sequences. (Running on oeis4.)