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

Author

Michel Marcus, Nov 13 2013

Keywords

• nonn

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.

Crossrefs

Cf. A231589.

Programs

PARI

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