A394729 a(n) is the smallest positive integer such that n^3 + a(n)^3 is a primitive taxicab number, or 0 if no such number exists.

12, 16, 60, 110, 76, 552, 474, 53, 10, 9, 93, 1, 5288, 207, 9, 2, 39, 139, 24, 97, 238, 57, 94, 19, 167, 36, 10, 791, 50, 67, 33, 166, 15, 2, 98, 26, 174, 43, 17, 12, 86, 69, 38, 2929, 196, 1275, 97, 69, 120, 29, 12, 974, 8, 24, 17, 61, 22, 9, 22, 3, 56, 109

Offset

1,1

Comments

Here, a "taxicab number" refers to a number which can be written as the sum of two positive cubes in two different ways (A001235). A "primitive taxicab number" is some taxicab number a^3 + b^3 = c^3 + d^3 such that gcd(a,b,c,d) = 1 (A018850).

Is 0 ever in this sequence?

Links

Robin Jones, Table of n, a(n) for n = 1..10000

Example

a(1) = 12 as 1729 = 1^3 + 12^3 is a primitive taxicab number, and none of 1^3 + 1^3, 1^3 + 2^3, ..., 1^3 + 11^3 are primitive taxicab numbers.

Crossrefs

Cf. A001235, A018850.

Sequence in context: A219390 A050585 A377906 * A050555 A060669 A166644

Adjacent sequences: A394726 A394727 A394728 * A394730 A394731 A394732

Keyword

nonn

Author

Robin Jones, Mar 30 2026

Status

approved