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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
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 (list; graph; refs; listen; history; text; internal format)
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 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

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])||#a<2, L+1, a[#a]+a[#a-1]))); if(type(show)=="t_VEC", a, a[#a])}

CROSSREFS

Sequence in context: A104205 A267758 A166015 * A021428 A238207 A050196

Adjacent sequences:  A268131 A268132 A268133 * A268135 A268136 A268137

KEYWORD

nonn,look

AUTHOR

M. F. Hasler, Jan 26 2016

STATUS

approved

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Last modified October 17 18:58 EDT 2019. Contains 328127 sequences. (Running on oeis4.)