A231791 Integers k such that A231589(k) = floor(k*(k-1)/4) - k.

8, 25, 77, 125, 133, 209, 301, 325, 425, 469, 473, 725, 737, 817, 925, 1025, 1141, 1273, 1325, 1525, 1625, 1793, 1825, 2125, 2225, 2425, 2525, 2725, 2825, 2881, 3097, 3425, 3625, 3725, 3925, 4325, 4525, 4625, 4825, 4925, 5125, 5525, 5725, 5825, 6025, 6425

Offset

1,1

Comments

It appears that this sequence is the union of 3 sets.

First term is 8, and is the only even known value.

Then we get terms that are equal to 25 * b with b a squarefree product of primes congruent to 1 modulo 4 (A002144), that is, terms of A231754.

And we get the following terms 77, 133, 209, 301, 469, 473, 737, 817, 1141, 1273, 1793, 2881, 3097, 7009, 10921. These numbers are the products of 2 distinct primes from this list: 7, 11, 19, 43, 67, 163 (a subsequence of A003173).

Links

Hugo Pfoertner, Table of n, a(n) for n = 1..10000

John P. Robertson, Shirali’s Questions About Sums of Residues of Squares

S. A. Shirali, A family portrait of primes-a case study in discrimination, Math. Mag. Vol. 70, No. 4 (Oct., 1997), pp. 263-272.

Prog

(PARI) isok(n) = A231589(n) == n*(n-1)/4 - n;

Crossrefs

Cf. A231589.

Sequence in context: A287120 A127813 A295911 * A035073 A041120 A042637

Adjacent sequences: A231788 A231789 A231790 * A231792 A231793 A231794

Keyword

nonn

Author

Michel Marcus, Nov 13 2013

Status

approved