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

1,2

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[#a-1]))); a}

Crossrefs

Sequence in context: A376685 A085181 A374351 * A185725 A359804 A378233

Adjacent sequences: A268126 A268127 A268128 * A268130 A268131 A268132

Keyword

nonn

Author

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

Status

approved