A138609 - OEIS

%I #12 Feb 10 2023 14:29:42

%S 1,3,4,2,5,6,7,8,11,12,9,10,13,14,17,15,16,19,20,23,24,18,21,22,25,26,

%T 29,30,27,28,31,32,35,36,39,40,33,34,37,38,41,42,45,46,49,43,44,47,48,

%U 51,52,55,56,59,60,50,53,54,57,58,61,62,65,66,69,70,63,64,67,68,71,72

%N List the first term from A042963, then 2 terms from A014601 (starting from 3), 3 terms from A042963, 4 terms from A014601, etc.

%C The original name was "Generalized Connell sequence". However, this sequence has only a passing resemblance to Connell-like sequences (see A001614 and the paper by Iannucci & Mills-Taylor), which are all monotone, while this sequence is a bijection of natural numbers.

%C The sequence is formed by concatenating subsequences S1,S2,S3,..., each of finite length. The subsequence S1 consists of the element 1. The n-th subsequence has n elements. Each subsequence is nondecreasing. The difference between two consecutive elements in the same subsequence is varying, but >= 1.

%H Douglas E. Iannucci and Donna Mills-Taylor, <a href="http://www.cs.uwaterloo.ca/journals/JIS/IANN/iann1.html">On Generalizing the Connell Sequence</a>, Journal of Integer Sequences, Vol. 2 (1999), Article 99.1.7

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

%F a(n) = A116966(A074147(n)-1). - _Antti Karttunen_, Oct 05 2009

%e Let us separate natural numbers into two disjoint sets (A042963 and A014601):

%e   1,2,5,6,9,10,13,14,17,18,21,22,25,26,29,30,...

%e   3,4,7,8,11,12,15,16,19,20,23,24,27,28,31,32,...

%e then

%e   S1={1}

%e   S2={3,4}

%e   S3={2,5,6,}

%e   S4={7,8,11,12}

%e   S5={9,10,13,14,17}

%e   ...

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

%Y Inverse: A166016. Cf. A138606, A138607, A138608, A138612.

%K nonn,tabl,easy

%O 1,2

%A _Ctibor O. Zizka_, May 14 2008

%E Edited, extended and keyword tabl added by _Antti Karttunen_, Oct 05 2009