A138609 - OEIS

A138609

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

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, 29, 30, 27, 28, 31, 32, 35, 36, 39, 40, 33, 34, 37, 38, 41, 42, 45, 46, 49, 43, 44, 47, 48, 51, 52, 55, 56, 59, 60, 50, 53, 54, 57, 58, 61, 62, 65, 66, 69, 70, 63, 64, 67, 68, 71, 72

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OFFSET

1,2

COMMENTS

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.

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.

LINKS

Table of n, a(n) for n=1..72.

Douglas E. Iannucci and Donna Mills-Taylor, On Generalizing the Connell Sequence, Journal of Integer Sequences, Vol. 2 (1999), Article 99.1.7

Index entries for sequences that are permutations of the natural numbers

FORMULA

a(n) = A116966(A074147(n)-1). - Antti Karttunen, Oct 05 2009

EXAMPLE

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

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

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

then

S1={1}