A155561 Intersection of A000404 and A154777: N = a^2 + b^2 = c^2 + 2d^2 with a,b,c,d>0.

17, 18, 34, 41, 68, 72, 73, 82, 89, 97, 113, 136, 137, 146, 153, 162, 164, 178, 193, 194, 225, 226, 233, 241, 242, 257, 272, 274, 281, 288, 289, 292, 306, 313, 328, 337, 353, 356, 369, 386, 388, 401, 409, 425, 433, 449, 450, 452, 457, 466, 482, 514, 521, 544

Offset: 1

Author

M. F. Hasler, Jan 24 2009

Keywords

• easy
• nonn

Examples

			a(1)=17 is the least number that can be written as A+B and C+2D where A,B,C,D are positive squares (namely 17 = 1^2 + 4^2 = 3^2 + 2*2^2).
a(2)=18 is the second smallest number which figures in A000404 and in A154777 as well.
		

Programs

PARI

isA155561(n,/* use optional 2nd arg to get other analogous sequences */c=[2,1]) = { for( i=1,#c, for( b=1,sqrtint((n-1)\c[i]), issquare(n-c[i]*b^2) & next(2)); return);1}
for( n=1,10^3, isA155561(n) & print1(n","))