A155564 Intersection of A002479 and A003136: N = a^2 + 2b^2 = c^2 + 3d^2 for some integers a,b,c,d.

0, 1, 3, 4, 9, 12, 16, 19, 25, 27, 36, 43, 48, 49, 57, 64, 67, 73, 75, 76, 81, 97, 100, 108, 121, 129, 139, 144, 147, 163, 169, 171, 172, 192, 193, 196, 201, 211, 219, 225, 228, 241, 243, 256, 268, 283, 289, 291, 292, 300, 304, 307, 313, 324, 331, 337, 361, 363

Offset: 1

Author

M. F. Hasler, Jan 25 2009

Keywords

• easy
• nonn

Comments

Contains A155574 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

isA155564(n,/* use optional 2nd arg to get other analogous sequences */c=[3,2]) = { 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, isA155564(n) & print1(n","))