A342042 -id:A342042 - cp's OEIS frontend

A377916 Inverse permutation to A377915.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 18, 19, 21, 22, 24, 25, 26, 28, 29, 31, 32, 34, 14, 35, 36, 37, 38, 40, 41, 43, 44, 46, 47, 48, 50, 51, 53, 17, 27, 39, 54, 55, 56, 57, 59, 60, 62, 63, 64, 66, 20, 30, 42, 49, 58, 67, 68, 69, 70, 72, 73, 23, 33, 45, 52, 61, 65, 71, 74, 75, 76, 77, 78, 80, 81, 83, 84, 86, 87, 89, 90, 91, 92, 95, 96, 100, 101, 104, 105, 109

Offset: 1

N. J. A. Sloane, Nov 29 2024

See A377915 for further information.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program
Index entries for sequences that are permutations of the natural numbers

Cf. A342042, A377912, A377915.

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A366113 A fractal sequence. Pick any term t: exactly one of the t terms following t is larger than t.

Original entry on oeis.org

1, 2, 1, 3, 1, 2, 4, 1, 2, 1, 5, 1, 2, 1, 3, 6, 1, 2, 1, 3, 1, 7, 1, 2, 1, 3, 1, 2, 8, 1, 2, 1, 3, 1, 2, 4, 9, 1, 2, 1, 3, 1, 2, 4, 1, 10, 1, 2, 1, 3, 1, 2, 4, 1, 2, 11, 1, 2, 1, 3, 1, 2, 4, 1, 2, 1, 12, 1, 2, 1, 3, 1, 2, 4, 1, 2, 1, 5, 13, 1, 2, 1, 3, 1, 2, 4, 1, 2, 1, 5, 1, 14

Offset: 1

Eric Angelini, Sep 29 2023

nonn

Starting with a(1) = 1, this is the lexicographically earliest sequence with this property.
This is how the sequence was built:
1) start with the Natural numbers and increase the gaps between them by one unit (first gap is zero):
S = 1,2,,3,,_,4,,,_,5,,,_,,6,,_,,,_,7,,,_,,,_,8, …
2) fill the empty spaces with the successive starting chunks of the sequence S itself:
S = 1,2,,3,,_,4,,,_,5,,,_,,6,,_,,,_,7,,,_,,,_,8,_, …
S = 1,2,1,3,,,4,,,_,5,,,_,,6,,_,,,_,7,,,_,,,_,8,_, …
S = 1,2,1,3,1,2,4,,,_,5,,,_,,6,,_,,,_,7,,,_,,,_,8,_, …
S = 1,2,1,3,1,2,4,1,2,1,5,,,_,,6,,_,,,_,7,,,_,,,_,8,_, …
S = 1,2,1,3,1,2,4,1,2,1,5,1,2,1,3,6,,,_,,,7,,,_,,,_,8,_, …
S = 1,2,1,3,1,2,4,1,2,1,5,1,2,1,3,6,1,2,1,3,1,7,,,_,,,_,8,_, …
S = 1,2,1,3,1,2,4,1,2,1,5,1,2,1,3,6,1,2,1,3,1,7,1,2,1,3,1,2,8,_, … Etc.

			One term out of 1 following a(1) = 1 is larger than 1: this is 2.
One term out of 2 following a(2) = 2 is larger than 2: this is 3.
One term out of 1 following a(3) = 1 is larger than 1: this is 2.
One term out of 3 following a(4) = 3 is larger than 3: this is 4.
One term out of 1 following a(5) = 1 is larger than 1: this is 2.
One term out of 2 following a(6) = 2 is larger than 2: this is 4.
One term out of 4 following a(7) = 4 is larger than 4: this is 5.
One term out of 1 following a(8) = 1 is larger than 1: this is 2.
One term out of 2 following a(9) = 2 is larger than 2: this is 5. Etc.

Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000

Cf. A342042.

k=1;Nest[(k++;Join[#,#[[;;k-2]],{k}])&,{1},13] (* Giorgos Kalogeropoulos, Oct 03 2023 *)

Data corrected by Giorgos Kalogeropoulos, Oct 03 2023

cp's OEIS Frontend

A377916 Inverse permutation to A377915.

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