A175428 a(n) is the smallest positive integer such that a(n)+a(n-1) is a cube and a(n) is not in {a(1), ..., a(n-1)}.

1, 7, 20, 44, 81, 135, 208, 8, 19, 45, 80, 136, 207, 9, 18, 46, 79, 137, 206, 10, 17, 47, 78, 138, 205, 11, 16, 48, 77, 139, 204, 12, 15, 49, 76, 140, 203, 13, 14, 50, 75, 141, 202, 310, 33, 31, 94, 122, 3, 5, 22, 42, 83, 133, 210, 6, 2, 25, 39, 86, 130, 213, 299, 430, 82

Offset: 1

Author

John W. Layman, May 10 2010

Keywords

• nonn
• easy

Comments

It appears that this is a permutation of the positive integers. 4 occurs as a(149).

See A034175 for the case where a(n)+a(n-1) is a square.

The parity of a(n) equals A133872(n) until n=56 after which there are occasional deviations from the pattern. This is clearly shown by considering the run lengths of the parity for this sequence: 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,2,2,2,2,2,2,2,1,2,3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,2,2,1,2,2,2,1,2,2,3,2,1,2,2,2,3,2,2,2,2,2,2,1,2,2,2,1,2,3,2,2,2,3,2,2,1,2,2,1,... - Jeremy Gardiner, Feb 16 2014

Links

• Jeremy Gardiner, Table of n, a(n) for n = 1..1319

Crossrefs

Cf. A034175, A011934, A000578 (the cubes), A133872.

Programs

Mathematica

a = {1}; For[i = 2, i < 66, i++, k = 1; While[! IntegerQ@ Power[k + a[[i - 1]] && ! MemberQ[a, k], 1/3], k++]; AppendTo[a, k]]; a (* Michael De Vlieger, Jun 02 2015 *)

PARI

v=[1];n=1;while(n<10^3,if(ispower((v[#v]+n),3)&&!vecsearch(vecsort(v),n),v=concat(v,n);n=0);n++);v \\ Derek Orr, Jun 01 2015