A138612 -id:A138612 - cp's OEIS frontend

A166017 Inverse permutation of A138612.

1, 2, 4, 3, 7, 11, 5, 16, 22, 29, 8, 6, 37, 46, 12, 56, 67, 79, 9, 17, 92, 106, 23, 121, 137, 13, 30, 10, 154, 172, 191, 211, 38, 232, 18, 254, 47, 277, 14, 301, 326, 24, 57, 352, 379, 68, 407, 436, 31, 80, 466, 19, 15, 497, 529, 562, 93, 596, 631, 39, 107, 667, 704

Offset: 1

Antti Karttunen, Oct 05 2009

nonn

Index entries for sequences that are permutations of the natural numbers

Inverse: A138612.

A166018 Left edge of triangular table A138612.

Original entry on oeis.org

1, 2, 3, 5, 6, 8, 9, 10, 13, 14, 16, 17, 18, 21, 22, 24, 25, 29, 30, 31, 32, 34, 36, 38, 40, 41, 44, 45, 47, 48, 51, 54, 55, 56, 58, 59, 62, 63, 65, 67, 69, 72, 73, 74, 75, 77, 80, 81, 83, 84, 87, 89, 92, 94, 96, 98, 99, 100, 102, 103, 104, 109, 110, 111, 113, 116, 118

Offset: 1

Antti Karttunen, Oct 05 2009

nonn

a(n) = A138612(A000124(n-1)).

A166019 Right edge of triangular table A138612.

Original entry on oeis.org

1, 4, 12, 28, 53, 91, 141, 207, 297, 401, 534, 683, 869, 1081, 1327, 1601, 1912, 2275, 2665, 3095, 3569, 4110, 4682, 5314, 5996, 6744, 7535, 8394, 9320, 10303, 11367, 12490, 13686, 14938, 16288, 17707, 19227, 20808, 22490, 24233, 26103, 28033

Offset: 1

Antti Karttunen, Oct 05 2009

nonn

a(n) = A138612(A000217(n)).

A166020 Row sums of triangular table A138612.

Original entry on oeis.org

1, 6, 22, 63, 139, 277, 481, 785, 1256, 1851, 2688, 3692, 5055, 6731, 8797, 11239, 14175, 17834, 21947, 26701, 32181, 38769, 46002, 54364, 63742, 74455, 86182, 99345, 114094, 130213, 148293, 167991, 189584, 212705, 238497, 266350, 297058

Offset: 1

Antti Karttunen, Oct 05 2009

nonn

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.

Original entry on oeis.org

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

Ctibor O. Zizka, May 14 2008

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

			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.

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

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 *)

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

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

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

A138608 List first F(1) numbers from A016777, then first F(2) numbers from A016789, then the first F(3) numbers from A008585 (starting from 3), then the next F(4) numbers from A016777, then the next F(5) numbers from A016789, then the next F(6) numbers from A008585, etc, where F(n) = A000045(n), the n-th Fibonacci number.

Original entry on oeis.org

1, 2, 3, 6, 4, 7, 10, 5, 8, 11, 14, 17, 9, 12, 15, 18, 21, 24, 27, 30, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84

Offset: 1

Ctibor O. Zizka, May 14 2008

The original name was "Generalized FibCon 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.

			Let us separate natural numbers into three disjoint sets (A016777, A016789 and A008585):
  1,4,7,10,13,16,19,22,25,28,31,...
  2,5,8,11,14,17,20,23,26,29,32,...
  3,6,9,12,15,18,21,24,27,30,33,...
then
  S0={1}
  S1={2}
  S2={3,6}
  S3={4,7,10}
  S4={5,8,11,14,17}
  S5={9,12,15,18,21,24,27,30}
  ...
and concatenating S0/S1/S2/S3/S4/S5/... gives this sequence.

Douglas E. Iannucci, 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: A166015. A010872(a(n)) = A010872(A072649(n)). Cf. A138606-A138609, A138612.

If n < 4, a(n) = n. If n = A000045(A072649(n)+1), then a(n) = a(n-1-A000045(A072649(n)))+3, otherwise a(n) = a(n-1)+3. - Antti Karttunen, Oct 05 2009

1. The sequence is formed by concatenating subsequences S0,S1, S2, ..., each of finite length. 2. The subsequence S0 consists of the element 1. 3. The n-th subsequence has F(n) elements, F(n) denotes n-th Fibonacci number. 4. Each subsequence is nondecreasing and the difference between two consecutive elements in the same subsequence is 3.

Edited, extended, starting offset changed from 0 to 1, and Scheme-code added by Antti Karttunen, Oct 05 2009

cp's OEIS Frontend

A166017 Inverse permutation of A138612.

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A166018 Left edge of triangular table A138612.

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A166019 Right edge of triangular table A138612.

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A166020 Row sums of triangular table A138612.

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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.

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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.

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