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%I #7 Jan 27 2016 12:22:48
%S 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,
%T 24,46,25,26,27,53,28,30,58,31,32,33,65,35,36,71,37,38,39,77,40,42,82,
%U 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
%N 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.
%C 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).
%H M. F. Hasler, <a href="/A268129/b268129.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%o (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[#a-1])));a}
%K nonn
%O 1,2
%A _Eric Angelini_, _Lars Blomberg_ and _M. F. Hasler_, Jan 26 2016
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