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 A230044 Nonnegative numbers k such that k plus a perfect square is a triangular number. 10
 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 k 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, ... Conjecture: these are the sorted distinct terms 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 Cf. A035251, A064784, A175035. Sequence in context: A131292 A276476 A069880 * A329269 A069861 A047449 Adjacent sequences:  A230041 A230042 A230043 * A230045 A230046 A230047 KEYWORD nonn AUTHOR Ralf Stephan, Oct 06 2013 STATUS approved

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Last modified January 21 00:46 EST 2022. Contains 350473 sequences. (Running on oeis4.)