A359030 - OEIS

%I #21 Dec 21 2022 04:50:10

%S 9,27,36,57,72,99,132,153,216,219,243,288,297,324,369,387,405,408,456,

%T 489,495,531,576,603,612,645,684,729,792,855,867,963,972,996,1017,

%U 1056,1071,1125,1179,1197,1224,1233,1353,1368,1407,1455,1476,1539,1548,1584,1701,1728,1737,1752,1845,1881

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

%C 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 In contrast to A306213, the arithmetic progression need not consist only of positive numbers.

%H Robert Israel, <a href="/A359030/b359030.txt">Table of n, a(n) for n = 1..10000</a>

%e a(4) = 57 is a term because 57 = (-2)^3 + 1^3 + 4^3 where (-2, 1, 3) are in arithmetic progression.

%p N:= 2000: # for terms <= N

%p L:= NULL:

%p for a from 1 while 3*a^3 <= N do

%p   for b from 1 do

%p     x:= 3*a*(a^2 + 2*b^2);

%p     if x > N then break fi;

%p     L:= L,x

%p od od:

%p sort(convert({L},list));

%Y Cf. A306213, A359078.

%K nonn

%O 1,1

%A _Robert Israel_, Dec 15 2022