A121878 a(1)=1. a(n) = the smallest positive integer not occurring earlier in the sequence such that a(n-1)+a(n) is squarefree.

1, 2, 3, 4, 6, 5, 8, 7, 10, 9, 12, 11, 15, 14, 16, 13, 17, 18, 19, 20, 21, 22, 24, 23, 28, 25, 26, 27, 30, 29, 32, 33, 34, 31, 35, 36, 37, 40, 38, 39, 43, 42, 41, 44, 45, 46, 47, 48, 49, 52, 50, 51, 54, 53, 56, 55, 58, 57, 61, 62, 60, 59, 63, 64, 65, 66, 67, 70, 68, 69, 72, 71

Offset: 1

Author

Leroy Quet, Aug 31 2006

Keywords

• nonn

Comments

Inverse: A167905; A167904(n) = a(a(n)). [Reinhard Zumkeller, Nov 15 2009]

Conjectured to be a permutation of the natural numbers. - Derek Orr, Jun 01 2015

Examples

			9,10,11,12,... are the positive integers not occurring among the first 8 terms of the sequence. a(8) + 9 = 16, which is not squarefree. a(8) + 10 = 17, which is squarefree. So a(9) = 10.
		

Links

• Scott R. Shannon, Table of n, a(n) for n = 1..10000
• Index entries for sequences that are permutations of the natural numbers [_Reinhard Zumkeller_, Nov 15 2009]

Crossrefs

Cf. A167907, A075380. [Reinhard Zumkeller, Nov 15 2009]

Programs

Mathematica

f[s_] := Block[{k = 1},While[MemberQ[s, k] || Max @@ Last /@ FactorInteger[(s[[ -1]] + k)] > 1, k++ ]; Append[s, k]]; Nest[f, {1}, 75] (* Ray Chandler, Sep 06 2006 *)

PARI

v=[1];n=1;while(n<100,if(issquarefree(v[#v]+n)&&!vecsearch(vecsort(v),n),v=concat(v,n);n=0);n++);v \\ Derek Orr, Jun 01 2015

Extensions

Extended by Ray Chandler, Sep 06 2006