login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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