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 A268129 If a(n) is a multiple of 3, then a(n+1) = a(n) + a(n-1). 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 (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 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 PROG (PARI) {a(n, show=1, a=[1], L=0/*up to L all numbers are used*/, U=[]/*numbers > L already used*/)=while(#aL+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[#a-1]))); 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

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Last modified October 20 05:42 EDT 2019. Contains 328247 sequences. (Running on oeis4.)