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A155578 Intersection of A000404 and A155717: N = a^2 + b^2 = c^2 + 7*d^2 for some positive integers a,b,c,d.

%I A155578 #10 Aug 29 2021 02:46:46
%S A155578 8,29,32,37,53,72,109,113,116,128,137,148,149,193,197,200,212,232,233,
%T A155578 261,277,281,288,296,317,333,337,373,389,392,400,401,421,424,436,449,
%U A155578 452,457,464,477,512,541,548,557,569,592,596,613,617,641,648,653,673
%N A155578 Intersection of A000404 and A155717: N = a^2 + b^2 = c^2 + 7*d^2 for some positive integers a,b,c,d.
%C A155578 Subsequence of A155568 (where a,b,c,d may be zero).
%o A155578 (PARI) isA155578(n,/* optional 2nd arg allows us to get other sequences */c=[7,1]) = { for(i=1,#c, for(b=1,sqrtint((n-1)\c[i]), issquare(n-c[i]*b^2) & next(2)); return);1}
%o A155578 for( n=1,999, isA155578(n) & print1(n","))
%o A155578 (Python)
%o A155578 from math import isqrt
%o A155578 def aupto(limit):
%o A155578     cands = range(1, isqrt(limit)+1)
%o A155578     left =  set(a**2 +   b**2 for a in cands for b in cands)
%o A155578     right = set(c**2 + 7*d**2 for c in cands for d in cands)
%o A155578     return sorted(k for k in left & right if k <= limit)
%o A155578 print(aupto(673)) # _Michael S. Branicky_, Aug 29 2021
%Y A155578 Cf. A000404, A154777, A092572, A097268, A154778, A155716, A155717.
%K A155578 easy,nonn
%O A155578 1,1
%A A155578 _M. F. Hasler_, Jan 25 2009