A051384 Sum of two (possibly negative) cubes in at least 4 ways.

2741256, 4118877, 6017193, 6742008, 9016488, 16776487, 21930048, 28699272, 32951016, 36875384, 42549416, 48137544, 48275136, 52324993, 53936064, 70957971, 72131904, 74013912, 87539319, 94287375, 102977784, 105651000, 111209679, 119824488, 122262264, 124454421, 134211896

Offset: 1

Author

Colin Mallows

Keywords

• nonn
• changed

Comments

This sequence is infinite, since if n is in the sequence so is n*k^3 for all k > 0; thus a(n) << n^3. - Charles R Greathouse IV, Nov 29 2014

Examples

			42549416 = 348^3+74^3 = 282^3+272^3 = (-2662)^3+2664^3 = (-475)^3+531^3, so 42549416 is in the sequence. (Silverman)
		

Links

• Rosalie Fay, Table of n, a(n) for n = 1..100
• Joseph H. Silverman, Taxicabs and sums of two cubes, Amer. Math. Monthly, 100 (1993), 331-340.

Crossrefs

Cf. A051347, A051383.

Programs

PARI

T=thueinit('z^3+1);is(n)=my(v=thue(T, n)); #v>6 && #select(u->u[1]<=u[2],v)>3 \\ Charles R Greathouse IV, Nov 29 2014

Formula

a(1) = A047696(4). - R. J. Mathar, Aug 28 2025

Extensions

a(6)-a(22) from Donovan Johnson, Apr 17 2010

Missing terms 42549416, 48275136, 94287375, 111209679, 124454421 added by Rosalie Fay, Oct 13 2017