A155568 Intersection of A001481 inter A020670: N = a^2 + b^2 = c^2 + 7d^2 for some integers a,b,c,d.

0, 1, 4, 8, 9, 16, 25, 29, 32, 36, 37, 49, 53, 64, 72, 81, 100, 109, 113, 116, 121, 128, 137, 144, 148, 149, 169, 193, 196, 197, 200, 212, 225, 232, 233, 256, 261, 277, 281, 288, 289, 296, 317, 324, 333, 337, 361, 373, 389, 392, 400, 401, 421, 424, 436, 441, 449

Offset: 1

Author

M. F. Hasler, Jan 25 2009

Keywords

• easy
• nonn

Comments

Contains A155578 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

isA155568(n,/* use optional 2nd arg to get other analogous sequences */c=[7,1]) = { for(i=1,#c, for(b=0,sqrtint(n\c[i]), issquare(n-c[i]*b^2) & next(2)); return);1}
for( n=0,500, isA155568(n) & print1(n","))