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A359030 Positive numbers that are the sum of cubes of three distinct integers in arithmetic progression.

%I A359030 #21 Dec 21 2022 04:50:10
%S A359030 9,27,36,57,72,99,132,153,216,219,243,288,297,324,369,387,405,408,456,
%T A359030 489,495,531,576,603,612,645,684,729,792,855,867,963,972,996,1017,
%U A359030 1056,1071,1125,1179,1197,1224,1233,1353,1368,1407,1455,1476,1539,1548,1584,1701,1728,1737,1752,1845,1881
%N A359030 Positive numbers that are the sum of cubes of three distinct integers in arithmetic progression.
%C A359030 Numbers that can be represented in at least one way as 3*a*(a^2 + 2*b^2) for positive integers a and b.
%C A359030 In contrast to A306213, the arithmetic progression need not consist only of positive numbers.
%H A359030 Robert Israel, <a href="/A359030/b359030.txt">Table of n, a(n) for n = 1..10000</a>
%e A359030 a(4) = 57 is a term because 57 = (-2)^3 + 1^3 + 4^3 where (-2, 1, 3) are in arithmetic progression.
%p A359030 N:= 2000: # for terms <= N
%p A359030 L:= NULL:
%p A359030 for a from 1 while 3*a^3 <= N do
%p A359030   for b from 1 do
%p A359030     x:= 3*a*(a^2 + 2*b^2);
%p A359030     if x > N then break fi;
%p A359030     L:= L,x
%p A359030 od od:
%p A359030 sort(convert({L},list));
%Y A359030 Cf. A306213, A359078.
%K A359030 nonn
%O A359030 1,1
%A A359030 _Robert Israel_, Dec 15 2022