A155565 Intersection of A001481 and A020669: N = a^2 + b^2 = c^2 + 5d^2 for some integers a,b,c,d.

0, 1, 4, 5, 9, 16, 20, 25, 29, 36, 41, 45, 49, 61, 64, 80, 81, 89, 100, 101, 109, 116, 121, 125, 144, 145, 149, 164, 169, 180, 181, 196, 205, 225, 229, 241, 244, 245, 256, 261, 269, 281, 289, 305, 320, 324, 349, 356, 361, 369, 389, 400, 401, 404, 405, 409, 421

Offset: 1

Author

M. F. Hasler, Jan 25 2009

Keywords

• easy
• nonn

Comments

Contains A155575 as a subsequence (obtained by restricting a,b,c,d to be nonzero). Also contains A000290 (squares) as subsequence.

Crossrefs

Cf. A001481, A002479, A003136, A002481, A020668 ff.

Programs

PARI

isA155565(n,/* use optional 2nd arg to get other analogous sequences */c=[5,1]) = { for(i=1,#c, for(b=0,sqrtint(n\c[i]), issquare(n-c[i]*b^2) & next(2)); return);1}
for( n=1,500, isA155565(n) & print1(n","))