cp's OEIS Frontend

A380295 Numbers that can be written as a^2 + 3*b^2 for some a, b in A155716 and also as c^2 + 6*d^2 for some c, d in A092572.

%I A380295 #7 Jan 19 2025 12:00:39
%S A380295 1552,1975,4753,5047,5425,7825,8167,9175,10096,11025,11536,12007,
%T A380295 16528,16807,16993,18823,19600,23863,24832,25633,25767,26983,27223,
%U A380295 29200,30919,31600,31927,32791,33175,35329,35623,41953,43063,43687,51943,54775,57303,59575,60016,61783,63175,71575,72103
%N A380295 Numbers that can be written as a^2 + 3*b^2 for some a, b in A155716 and also as c^2 + 6*d^2 for some c, d in  A092572.
%C A380295 If k is a term, then so is j^4 * k for all positive integers j.
%H A380295 Robert Israel, <a href="/A380295/b380295.txt">Table of n, a(n) for n = 1..10000</a>
%e A380295 a(5) = 5425 is a term because 5425 = 73^2 + 6 * 4^2 = 25^2 + 3 * 40^2 with 73 = 5^2 + 3 * 4^2, 4 = 1^2 + 3 * 1^2, 25 = 1^2 + 6 * 2^2 and 40 = 4^2 + 6 * 2^2.
%p A380295 N:= 500: # for terms <= N^2
%p A380295 A:= {seq(seq(a^2 + 3*b^2,a=1..floor(sqrt(N-3*b^2))),b=1..floor(sqrt(N/3)))}:
%p A380295 B:= {seq(seq(a^2 + 6*b^2,a=1..floor(sqrt(N-6*b^2))),b=1..floor(sqrt(N/6)))}:
%p A380295 C:= select(`<=`,{seq(seq(a^2+6*b^2,a=A),b=A)},N^2):
%p A380295 E:= select(`<=`,{seq(seq(a^2+3*b^2,a=B),b=B)},N^2):
%p A380295 sort(convert(C intersect E,list));
%Y A380295 Cf. A092572, A155712, A155716.
%K A380295 nonn
%O A380295 1,1
%A A380295 _Robert Israel_, Jan 19 2025