A275335 The primes in the sequence appear in blocks and the successive sizes of these blocks are given by the sequence itself.

1, 2, 4, 3, 5, 6, 7, 11, 13, 17, 8, 9, 10, 12, 14, 15, 16, 18, 19, 23, 29, 20, 21, 22, 24, 25, 26, 27, 28, 30, 31, 37, 41, 43, 47, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 53, 59, 61, 67, 71, 73, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 79, 83, 89, 97, 101, 103, 107, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 102, 104, 105, 106, 108, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 110, 111

Offset

1,2

Comments

This is the lexicographically first such sequence starting with a(1)=1 and being always extended with the smallest integer not yet present that doesn't lead to a contradiction.

The sequence is a permutation of the integers > 0.

Links

Jean-Marc Falcoz, Table of n, a(n) for n = 1..23012

Example

The blocks of primes are indicated here by parentheses; the successive block-sizes are 1, 2, 4, 3, 5,... which reproduces the sequence itself:
1,(2),4,(3,5),6,(7,11,13,17),8,9,10,12,14,15,16,18,(19,23,29),20,21,22,24,25,26,27,28,30,(31,37,41,43,47),32,33,.

Mathematica

a = {1}; b = 1; c = Select[Range[10^4], CompositeQ]; Do[k = b + a[[i]] - 1; a = Join[a, Join[Prime@ Range[b, k], If[Prime@ b == 2, {4}, TakeWhile[c, # < NextPrime@ Prime@ k &] ] ]]; c = DeleteCases[c, k_ /; k <= Last@ a]; b = k + 1, {i, 8}]; a (* Michael De Vlieger, Jul 25 2016 *)

Crossrefs

Sequence in context: A274631 A368181 A375602 * A056019 A125963 A111269

Adjacent sequences: A275332 A275333 A275334 * A275336 A275337 A275338

Keyword

nonn,base

Author

Eric Angelini and Jean-Marc Falcoz, Jul 23 2016

Status

approved