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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. 14
 8, 29, 32, 37, 53, 72, 109, 113, 116, 128, 137, 148, 149, 193, 197, 200, 212, 232, 233, 261, 277, 281, 288, 296, 317, 333, 337, 373, 389, 392, 400, 401, 421, 424, 436, 449, 452, 457, 464, 477, 512, 541, 548, 557, 569, 592, 596, 613, 617, 641, 648, 653, 673 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Subsequence of A155568 (where a,b,c,d may be zero). LINKS PROG (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} for( n=1, 999, isA155578(n) & print1(n", ")) (Python) from math import isqrt def aupto(limit):     cands = range(1, isqrt(limit)+1)     left =  set(a**2 +   b**2 for a in cands for b in cands)     right = set(c**2 + 7*d**2 for c in cands for d in cands)     return sorted(k for k in left & right if k <= limit) print(aupto(673)) # Michael S. Branicky, Aug 29 2021 CROSSREFS Cf. A000404, A154777, A092572, A097268, A154778, A155716, A155717. Sequence in context: A298290 A298490 A299183 * A115107 A298217 A299093 Adjacent sequences:  A155575 A155576 A155577 * A155579 A155580 A155581 KEYWORD easy,nonn AUTHOR M. F. Hasler, Jan 25 2009 STATUS approved

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Last modified June 30 15:29 EDT 2022. Contains 354943 sequences. (Running on oeis4.)