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