A138606 List first F(1) odd numbers, then first F(2) even numbers (starting from 2), then the next F(3) odd numbers, then the next F(4) even numbers, etc., where F(n) = A000045(n), the n-th Fibonacci number.

1, 2, 3, 5, 4, 6, 8, 7, 9, 11, 13, 15, 10, 12, 14, 16, 18, 20, 22, 24, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77

Offset

1,2

Comments

The original name was "FibCon sequence". However, this sequence has only a passing resemblance to Connell-like sequences (see A001614), which are all monotone, while this sequence is a bijection of natural numbers.

Fixed points of the permutation are the terms of A062114. - Ivan Neretin, Sep 04 2017

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Index entries for sequences that are permutations of the natural numbers

Formula

a(n) = A166012(A072649(n)-1) + 2*(n - A000045(1+A072649(n))). - Antti Karttunen, Oct 05 2009

Example

Let us separate the positive integers into odd (A005408) and even numbers (A005843):
1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,...
2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,...
then we get the following subsequences:
S1={1}
S2={2}
S3={3,5}
S4={4,6,8}
S5={7,9,11,13,15}
S6={10,12,14,16,18,20,22,24}
...
and concatenating them S1/S2/S3/S4/S5/... gives this sequence.

Mathematica

o = 1; e = 2; Flatten@Table[If[OddQ[n], Range[o, (o += 2 Fibonacci[n]) - 1, 2], Range[e, (e += 2 Fibonacci[n]) - 1, 2]], {n, 9}] (* Ivan Neretin, Sep 04 2017 *)

Prog

(MIT Scheme:) (define (A138606 n) (if (zero? n) n (+ (A166012 (-1+ (A072649 n))) (* 2 (- n (A000045 (1+ (A072649 n))))))))

Crossrefs

Inverse: A166013. A000035(a(n)) = A000035(A072649(n)). Cf. A138607-A138609, A138612.

Sequence in context: A361314 A366474 A380350 * A166013 A089864 A073290

Adjacent sequences: A138603 A138604 A138605 * A138607 A138608 A138609

Keyword

easy,nonn

Author

Ctibor O. Zizka, May 14 2008

Extensions

Edited, extended and Scheme code added by Antti Karttunen, Oct 05 2009

Status

approved