A082982 Numbers k such that k, k+1 and k+2 are sums of 2 squares.

0, 8, 16, 72, 80, 144, 232, 288, 360, 520, 576, 584, 800, 808, 1088, 1096, 1152, 1224, 1312, 1600, 1664, 1744, 1800, 1872, 1960, 2248, 2304, 2312, 2384, 2592, 2600, 2824, 3328, 3392, 3528, 3600, 4112, 4176, 4328, 4624, 5120, 5184, 5328, 5408, 5904, 6056

Offset: 1

Author

Xavier Xarles (xarles(AT)mat.uab.es), May 28 2003

Keywords

• easy
• nonn

Comments

All terms are multiples of 8, cf. A304441. - M. F. Hasler, May 13 2018

Examples

			80 is here because 80=4^2+8^2, 81=0^2+9^2 and 82=1^2+9^2.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000
• Ajai Choudhry and Bibekananda Maji, Finite sequences of integers expressible as sums of two squares, arXiv:2310.13317 [math.NT], 2023.

Crossrefs

Cf. A001481, A050795, A304441.

Programs

PARI

issumsq(n) = {ok = 0; for (i=0, ceil(sqrt(n/2)), if (issquare(n - i^2), return (1));); return (0);}
isok(n) = issumsq(n) && issumsq(n+1) && issumsq(n+2) \\ Michel Marcus, Jun 30 2013

PARI

is_A082982(n)={n%8==0&&is_A001481(n\8)&&is_A001481(n\2+1)&&is_A001481(n+1)} \\ using is_A001481 is much faster than the issumsq() above. - M. F. Hasler, May 13 2018

Formula

a(n) = 8*A304441(n). - M. F. Hasler, May 13 2018

Extensions

More terms from Michel Marcus, Jun 30 2013