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

%I A155561 #5 Jun 02 2025 01:19:06
%S A155561 17,18,34,41,68,72,73,82,89,97,113,136,137,146,153,162,164,178,193,
%T A155561 194,225,226,233,241,242,257,272,274,281,288,289,292,306,313,328,337,
%U A155561 353,356,369,386,388,401,409,425,433,449,450,452,457,466,482,514,521,544
%N A155561 Intersection of A000404 and A154777: N = a^2 + b^2 = c^2 + 2d^2 with a,b,c,d>0.
%e A155561 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).
%e A155561 a(2)=18 is the second smallest number which figures in A000404 and in A154777 as well.
%o A155561 (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}
%o A155561 for( n=1,10^3, isA155561(n) & print1(n","))
%K A155561 easy,nonn
%O A155561 1,1
%A A155561 _M. F. Hasler_, Jan 24 2009