A268131 If a(n) is not squarefree, then a(n+1) = a(n) + a(n-1), else a(n+1) is the smallest positive integer not occurring earlier.

1, 2, 3, 4, 7, 5, 6, 8, 14, 9, 23, 10, 11, 12, 23, 13, 15, 16, 31, 17, 18, 35, 19, 20, 39, 21, 22, 24, 46, 25, 71, 26, 27, 53, 28, 81, 109, 29, 30, 32, 62, 33, 34, 36, 70, 37, 38, 40, 78, 41, 42, 43, 44, 87, 45, 132, 177, 47, 48, 95, 49, 144, 193, 50, 243

Offset

1,2

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 "lines" here (when the property occurs for consecutive terms), roughly proportional to n, 2n, 3n, ... Here we also have duplicate terms (which we could exclude explicitly), for n <= 1000 this happens 19 times.

Links

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

Prog

(PARI) {a(n, show=0, is=x->issquarefree(x), a=[1], L=0, U=[])->while(#a<n, show&&if(type(show)=="t_STR", write(show, #a, " ", a[#a]), print1(a[#a]", ")); if(a[#a]>L+1, U=setunion(U, [a[#a]]), L++; while(#U&&U[1]<=L+1, U=U[^1]; L++)); a=concat(a, if(is(a[#a]), L+1, a[#a]+a[#a-1]))); if(type(show)=="t_VEC", a, a[#a])}

Crossrefs

Sequence in context: A071665 A071662 A125978 * A361646 A359051 A014321

Adjacent sequences: A268128 A268129 A268130 * A268132 A268133 A268134

Keyword

nonn,look

Author

M. F. Hasler, Jan 26 2016

Status

approved