A076115 Squares (or 0) from A076114.

1, 9, 9, 0, 25, 81, 49, 36, 81, 225, 121, 0, 169, 441, 225, 0, 289, 225, 361, 0, 441, 1089, 529, 324, 400, 1521, 729, 0, 841, 2025, 961, 784, 1089, 2601, 1225, 0, 1369, 3249, 1521, 900, 1681, 3969, 1849, 0, 2025, 4761, 2209, 0, 1225, 2025, 2601, 0, 2809, 2025

Offset

1,2

Links

Table of n, a(n) for n=1..54.

Example

a(2) = 4+5 = 9= 3^2. a(8)= 1+2+3+4+5+6+7+8 = 36 = 6^2.

Prog

(PARI) a(n) = if (!(n%4) && ((n/4^valuation(n, 4)) % 2), 0, my(o=n*(n+1)/2, k=0); while(!issquare(o+n*k), k++); o+n*k); \\ Michel Marcus, Sep 09 2025
(Python)
from itertools import count
from sympy.ntheory.primetest import is_square
def A076115(n):
    if not (n&1 or (~n & n-1).bit_length()&1): return 0
    return next(m for a in count(1) if is_square(m:=n*(n+(a<<1)-1)>>1)) # Chai Wah Wu, Sep 16 2025

Crossrefs

Cf. A001108, A001109, A076114.

Sequence in context: A090655 A334480 A229758 * A014726 A277069 A197503

Adjacent sequences: A076112 A076113 A076114 * A076116 A076117 A076118

Keyword

nonn

Author

Amarnath Murthy, Oct 09 2002

Extensions

More terms from David Wasserman, Apr 02 2005

Status

approved