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A230044 Nonnegative numbers n such that n plus a perfect square is a triangular number. 9
0, 1, 2, 3, 5, 6, 9, 10, 11, 12, 14, 15, 17, 19, 20, 21, 24, 27, 28, 29, 30, 32, 35, 36, 39, 41, 42, 44, 45, 46, 50, 51, 53, 54, 55, 56, 57, 62, 65, 66, 69, 71, 72, 74, 75, 77, 78, 80, 82, 84, 87, 89, 90, 91, 95, 96, 100, 101, 104, 105, 107, 109, 110, 111, 116, 117, 119, 120, 122, 126, 127, 128 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Negative n are in A175035.

Numbers such that the Diophantine equation y^2 + y - 2x^2 = 2n, y > 0 has a solution. Empirically, solutions (x,y) don't exceed (5n,5n) for n < 10^5. Record quotients y/n are at n = 2, 3, 12, 45, 1225, 6806, ...

Probably also the sorted unique members of A064784.

n is in this sequence iff 8n+1 is in A035251, that is, every prime p == 3 or 5 (mod 8) dividing 8n+1 appears to an even power. - Max Alekseyev, Oct 14 2013

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

EXAMPLE

28 is triangular, and 25 is a square <= 28, and 28-25=3, so 3 is in sequence.

PROG

(PARI) B=bnfinit(z^2-8); is(n)=#bnfisintnorm(B, 8*n+1) \\ Max Alekseyev, Oct 13 2013

CROSSREFS

Sequence in context: A131292 A276476 A069880 * A069861 A047449 A162923

Adjacent sequences:  A230041 A230042 A230043 * A230045 A230046 A230047

KEYWORD

nonn

AUTHOR

Ralf Stephan, Oct 06 2013

STATUS

approved

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Last modified November 15 18:29 EST 2019. Contains 329149 sequences. (Running on oeis4.)