A268134 If a(n) is squarefree (and n > 1), then a(n+1) = a(n) + a(n-1), else a(n+1) is the smallest positive integer not occurring earlier.

1, 2, 3, 5, 8, 4, 6, 10, 16, 7, 23, 30, 53, 83, 136, 9, 11, 20, 12, 13, 25, 14, 39, 53, 92, 15, 107, 122, 229, 351, 17, 368, 18, 19, 37, 56, 21, 77, 98, 22, 120, 24, 26, 50, 27, 28, 29, 57, 86, 143, 229, 372, 31, 403, 434, 837, 32, 33, 65, 98, 34, 132, 35, 167, 202, 369, 36, 38, 74, 112, 40, 41, 81, 42, 123, 165

Offset: 1

Author

M. F. Hasler, Jan 26 2016

Keywords

• nonn
• look

Comments

A variant of the sequence A267758 where the relation has to hold for prime numbers rather than for squarefree numbers. In contrast to that sequence we have many duplicate terms here (which we could exclude explicitely in order to get a permutation of the positive integers).

Links

• M. F. Hasler, Table of n, a(n) for n = 1..1000

Programs

PARI

{a(n,show=0,is=x->issquarefree(x),a=[1],L=0,U=[])=while(#aL+1,U=setunion(U,[a[#a]]),L++;while(#U&&U[1]<=L+1,U=U[^1];L++));a=concat(a,if(!is(a[#a])||#a<2,L+1,a[#a]+a[#a-1])));if(type(show)=="t_VEC",a,a[#a])}