

A268129


If a(n) is a multiple of 3, then a(n+1) = a(n) + a(n1). Lexicographic first permutation of the positive integers with this property.


1



1, 2, 3, 5, 4, 6, 10, 7, 8, 9, 17, 11, 12, 23, 13, 14, 15, 29, 16, 18, 34, 19, 20, 21, 41, 22, 24, 46, 25, 26, 27, 53, 28, 30, 58, 31, 32, 33, 65, 35, 36, 71, 37, 38, 39, 77, 40, 42, 82, 43, 44, 45, 89, 47, 48, 95, 49, 50, 51, 101, 52, 54, 106, 55, 56, 57, 113, 59, 60, 119, 61, 62, 63, 125, 64, 66, 130, 67, 68, 69, 137, 70, 72, 142, 73, 74, 75
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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 multiples of 3. In contrast to that sequence we only have two "bands" or lines here. L. Blomberg has studies several properties of this sequence (private communication).


LINKS

M. F. Hasler, Table of n, a(n) for n = 1..1000
Index entries for sequences that are permutations of the natural numbers


PROG

(PARI) {a(n, show=1, a=[1], L=0/*up to L all numbers are used*/, U=[]/*numbers > L already used*/)=while(#a<n, show&&print1(a[#a]", "); /*if the last term is larger than L+1, add it to U*/ if(a[#a]>L+1, U=setunion(U, [a[#a]]), /*else increase L and remove terms from U if possible*/ L++; while(#U&&U[1]<=L+1, U=U[^1]; L++)); a=concat(a, if(a[#a]%3, L+1, a[#a]+a[#a1]))); a}


CROSSREFS

Sequence in context: A185180 A175107 A085181 * A185725 A097347 A114744
Adjacent sequences: A268126 A268127 A268128 * A268130 A268131 A268132


KEYWORD

nonn


AUTHOR

Eric Angelini, Lars Blomberg and M. F. Hasler, Jan 26 2016


STATUS

approved



