A275582 The nonprime integers of the sequence appear in blocks. The successive sizes of these blocks are given by the sequence itself.

1, 2, 3, 4, 6, 5, 7, 8, 9, 10, 11, 12, 14, 15, 16, 13, 17, 18, 20, 21, 22, 24, 25, 19, 23, 26, 27, 28, 30, 32, 29, 31, 33, 34, 35, 36, 38, 39, 40, 37, 41, 42, 44, 45, 46, 48, 49, 50, 51, 43, 47, 52, 54, 55, 56, 57, 58, 60, 62, 63, 53, 59, 61, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 67, 71, 73, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 79, 83, 89, 91, 92, 93

Offset

1,2

Comments

The sequence is started with a(1)=1 and always extended with the smallest integer not yet used that doesn't lead to a contradiction.

The sequence is a permutation of the natural numbers.

Links

Table of n, a(n) for n=1..93.

Index entries for sequences that are permutations of the natural numbers

Example

The blocks of nonprime integers are indicated here by parentheses; the successive block-sizes are 1, 2, 3, 4, 6,... which reproduces the sequence itself: P = (1),2,3,(4,6),5,7,(8,9,10),11,(12,14,15,16),13,17,(18,20,21,22,24,25),19,23.

Mathematica

a[1]=1; a[n_]:=a[n]=Block[{k=1}, While[MemberQ[s=Array[a, n-1], k]||(g=Length/@Select[SplitBy[Join[s, {k}], !PrimeQ@#&], !PrimeQ@First@#&]; g!=s[[;; Length@g]]), If[!PrimeQ@k&&FreeQ[s, k], Break[], k++]]; k]; Array[a, 93] (* Giorgos Kalogeropoulos, May 12 2022 *)

Crossrefs

Sequence in context: A066115 A227788 A222245 * A129607 A130340 A130339

Adjacent sequences: A275579 A275580 A275581 * A275583 A275584 A275585

Keyword

nonn,base

Author

Eric Angelini, Aug 02 2016

Status

approved