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A275582
The nonprime integers of the sequence appear in blocks. The successive sizes of these blocks are given by the sequence itself.
0
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.
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
KEYWORD
nonn,base
AUTHOR
Eric Angelini, Aug 02 2016
STATUS
approved