A138608 -id:A138608 - cp's OEIS frontend

A166015 Inverse permutation to A138608.

1, 2, 3, 5, 8, 4, 6, 9, 13, 7, 10, 14, 21, 11, 15, 22, 12, 16, 23, 34, 17, 24, 35, 18, 25, 36, 19, 26, 37, 20, 27, 38, 55, 28, 39, 56, 29, 40, 57, 30, 41, 58, 31, 42, 59, 32, 43, 60, 33, 44, 61, 89, 45, 62, 90, 46, 63, 91, 47, 64, 92, 48, 65, 93, 49, 66, 94, 50, 67, 95, 51, 68

Offset: 1

Antti Karttunen, Oct 05 2009

nonn

Index entries for sequences that are permutations of the natural numbers

Inverse: A138608.

A138609 List the first term from A042963, then 2 terms from A014601 (starting from 3), 3 terms from A042963, 4 terms from A014601, etc.

Original entry on oeis.org

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

Offset: 1

Ctibor O. Zizka, May 14 2008

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.

			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}
  S2={3,4}
  S3={2,5,6,}
  S4={7,8,11,12}
  S5={9,10,13,14,17}
  ...
  and concatenating S1/S2/S3/S4/S5/... gives this sequence.

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

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

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

Edited, extended and keyword tabl added by Antti Karttunen, Oct 05 2009

A138607 List first A008578(1) odd numbers, then first A008578(2) even numbers, then the next A008578(3) odd numbers, then the next A008578(4) even numbers, etc.

Original entry on oeis.org

1, 2, 4, 3, 5, 7, 6, 8, 10, 12, 14, 9, 11, 13, 15, 17, 19, 21, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73

Offset: 1

Ctibor O. Zizka, May 14 2008

A permutation of numbers.

			Let
  S1={1}
  S2={2,4}
  S3={3,5,7}
  S4={6,8,10,12,14}
  S5={9,11,13,15,17,19,21}
  S6={16,18,20,22,24,26,28,30,32,34,36}
  ...
then S1, S2, S3, S4, S5, S6,... gives this sequence.

Index entries for sequences that are permutations of the natural numbers

Inverse: A166014. Cf. A138606, A138608, A138609, A138612.

If n < 3, a(n) = n. If n-2 = A007504(A083375(n-2)), then a(n) = a(n-1-A000040(A083375(n-2)))+2, otherwise a(n) = a(n-1)+2. - Antti Karttunen, Oct 05 2009.

Edited, extended, and offset changed from 0 to 1 by Antti Karttunen, Oct 05 2009

cp's OEIS Frontend

A166015 Inverse permutation to A138608.

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A138609 List the first term from A042963, then 2 terms from A014601 (starting from 3), 3 terms from A042963, 4 terms from A014601, etc.

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A138607 List first A008578(1) odd numbers, then first A008578(2) even numbers, then the next A008578(3) odd numbers, then the next A008578(4) even numbers, etc.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

Extensions