A155712 Intersection of A092572 and A155716: N = a^2 + 3b^2 = c^2 + 6d^2 for some positive integers a,b,c,d.

7, 28, 31, 49, 63, 73, 79, 97, 100, 103, 112, 124, 127, 151, 175, 193, 196, 199, 217, 223, 241, 252, 271, 279, 292, 313, 316, 337, 343, 367, 388, 400, 409, 412, 433, 439, 441, 448, 457, 463, 484, 487, 496, 508, 511, 553, 567, 577, 601, 604, 607, 631, 657, 673

Offset

1,1

Comments

From Robert Israel, Jan 19 2025: (Start)

If k is a term, then so is j^2 * k for all positive integers j.

The primes in this sequence appear to be A033199.

(End)

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

N:= 1000: # for terms <= N
A:= {seq(seq(a^2 + 3*b^2, b=1 .. floor(sqrt((N-a^2)/3))), a=1..floor(sqrt(N)))}
   intersect {seq(seq(c^2 + 6*d^2, d = 1 .. floor(sqrt((N-c^2)/6))), c=1..floor(sqrt(N)))}:
sort(convert(A, list)); # Robert Israel, Jan 19 2025

Prog

(PARI) isA155712(n, /* optional 2nd arg allows to get other sequences */c=[6, 3]) = { 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, isA155712(n) && print1(n", ")) \\ Update to modern PARI syntax (& -> &&) by M. F. Hasler, Jan 18 2025

Crossrefs

Cf. A000404, A033199, A092572, A097268, A154777, A154778, A155716, A155717, A155560-A155578.

Sequence in context: A200974 A184331 A267432 * A015817 A103253 A321777

Adjacent sequences: A155709 A155710 A155711 * A155713 A155714 A155715

Keyword

easy,nonn,changed

Author

M. F. Hasler, Jan 25 2009

Status

approved