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

9, 27, 36, 57, 72, 99, 132, 153, 216, 219, 243, 288, 297, 324, 369, 387, 405, 408, 456, 489, 495, 531, 576, 603, 612, 645, 684, 729, 792, 855, 867, 963, 972, 996, 1017, 1056, 1071, 1125, 1179, 1197, 1224, 1233, 1353, 1368, 1407, 1455, 1476, 1539, 1548, 1584, 1701, 1728, 1737, 1752, 1845, 1881

Offset

1,1

Comments

Numbers that can be represented in at least one way as 3*a*(a^2 + 2*b^2) for positive integers a and b.

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

Links

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

Example

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

Maple

N:= 2000: # for terms <= N
L:= NULL:
for a from 1 while 3*a^3 <= N do
  for b from 1 do
    x:= 3*a*(a^2 + 2*b^2);
    if x > N then break fi;
    L:= L, x
od od:
sort(convert({L}, list));

Crossrefs

Cf. A306213, A359078.

Sequence in context: A340237 A216168 A036303 * A325299 A353238 A116455

Adjacent sequences: A359027 A359028 A359029 * A359031 A359032 A359033

Keyword

nonn

Author

Robert Israel, Dec 15 2022

Status

approved