OFFSET
1,2
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
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
John W. Layman, May 10 2010
STATUS
approved