A085323 Numbers k such that both k and k+1 are sums of two positive cubes.

854, 4940, 9603, 10744, 17919, 29743, 62558, 79001, 133273, 164304, 193192, 205406, 214984, 242648, 263871, 378936, 431999, 447336, 488375, 517427, 610687, 731158, 762047, 1000511, 1061550, 1125207, 1134124, 1157632, 1158137, 1179520

Offset: 1

Author

Labos Elemer, Jul 01 2003

Keywords

• nonn

Comments

There are 664 terms < 8*10^9, a(664)=7999968373. - Zak Seidov, Jul 24 2009

This is an infinite sequence. To see why, consider the (N,N+1) pair N = 16*k^6 - 12*k^4 + 6*k^2 - 2 = (2*k^2 - k - 1)^3 + (2*k^2 + k -1)^3 and N + 1 = 16*k^6 - 12*k^4 + 6*k^2 - 1 = (2*k^2)^3 + (2*k^2 - 1)^3. - Ant King, Sep 20 2013

1796609972023999 is the smallest k such that k, k+1, and k+2 are sums of two positive cubes: k = 98978^3 + 93863^3, k+1 = 108620^3 + 80160^3, and k+2 = 120449^3 + 36628^3. - Giovanni Resta, May 07 2025

Examples

			854 = 9^3 + 5^3 and 855 = 8^3 + 7^3;
4940 = 17^3 + 3^3 and 4941 = 13^3 + 14^3.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..664

Crossrefs

Cf. A003325.

Programs

Mathematica

m=110; k=3; t=Union[Flatten[Table[Table[w^k+q^k, {w, q, m}], {q, 1, m}]]]; dt=Delete[ -RotateRight[t]+t, 1]; p=Part[t, Flatten[Position[dt, 1]]]; Select[p, # <= m^3 + 1 &] (* corrected by Giovanni Resta, May 09 2025 *)

Extensions

Corrected and extended by Zak Seidov, Jul 24 2009

Name and Example edited by Jon E. Schoenfield, Jul 29 2017