A138606 - OEIS

%I #20 Sep 05 2017 04:04:29

%S 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,

%T 29,31,33,35,37,39,41,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,

%U 58,60,62,64,66,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77

%N 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.

%C 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.

%C Fixed points of the permutation are the terms of A062114. - _Ivan Neretin_, Sep 04 2017

%H Ivan Neretin, <a href="/A138606/b138606.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F a(n) = A166012(A072649(n)-1) + 2*(n - A000045(1+A072649(n))). - _Antti Karttunen_, Oct 05 2009

%e Let us separate the positive integers into odd (A005408) and even numbers (A005843):

%e 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,...

%e 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,...

%e then we get the following subsequences:

%e S1={1}

%e S2={2}

%e S3={3,5}

%e S4={4,6,8}

%e S5={7,9,11,13,15}

%e S6={10,12,14,16,18,20,22,24}

%e ...

%e and concatenating them S1/S2/S3/S4/S5/... gives this sequence.

%t 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 *)

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

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

%K easy,nonn

%O 1,2

%A _Ctibor O. Zizka_, May 14 2008

%E Edited, extended and Scheme code added by _Antti Karttunen_, Oct 05 2009