A394729 - OEIS

%I #7 Apr 07 2026 00:35:22

%S 12,16,60,110,76,552,474,53,10,9,93,1,5288,207,9,2,39,139,24,97,238,

%T 57,94,19,167,36,10,791,50,67,33,166,15,2,98,26,174,43,17,12,86,69,38,

%U 2929,196,1275,97,69,120,29,12,974,8,24,17,61,22,9,22,3,56,109

%N 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.

%C 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).

%C Is 0 ever in this sequence?

%H Robin Jones, <a href="/A394729/b394729.txt">Table of n, a(n) for n = 1..10000</a>

%e 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.

%Y Cf. A001235, A018850.

%K nonn

%O 1,1

%A _Robin Jones_, Mar 30 2026