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

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

Offset

1,1

Comments

Subsequence of A155568 (where a,b,c,d may be zero).

Links

Table of n, a(n) for n=1..53.

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