

A268131


If a(n) is not squarefree, then a(n+1) = a(n) + a(n1), else a(n+1) is the smallest positive integer not occurring earlier.


1



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
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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[#a1]))); if(type(show)=="t_VEC", a, a[#a])}


CROSSREFS

Sequence in context: A071665 A071662 A125978 * A014321 A175343 A239965
Adjacent sequences: A268128 A268129 A268130 * A268132 A268133 A268134


KEYWORD

nonn,look


AUTHOR

M. F. Hasler, Jan 26 2016


STATUS

approved



