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, 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

Offset: 1

Author

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

Keywords

• nonn

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

Programs

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}