A274500 The odd integers in the sequence appear in blocks and the successive sizes of these blocks are given by the sequence itself.

1, 2, 3, 5, 4, 6, 7, 9, 11, 8, 10, 12, 13, 15, 17, 19, 21, 14, 16, 18, 20, 22, 23, 25, 27, 29, 24, 26, 28, 30, 31, 33, 35, 37, 39, 41, 32, 34, 36, 38, 40, 42, 43, 45, 47, 49, 51, 53, 55, 44, 46, 48, 50, 52, 54, 56, 57, 59, 61, 63, 65, 67, 69, 71, 73, 58, 60, 62, 64, 66, 68, 70, 72, 74, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 76, 78, 80, 82, 84, 86, 88, 90

Offset

1,2

Comments

The sequence starts with a(1)=1 and is always extended with the smallest integer not yet in the sequence which does not lead to a contradiction. The sequence is a permutation of the natural numbers.

Links

Zak Seidov, Table of n, a(n) for n = 1..10000

Zak Seidov, Color graph for n = 1..150.

Index entries for sequences that are permutations of the natural numbers

Example

The blocks of odd integers are indicated here by parentheses; the successive block-sizes are1,2,3,5,4,6,7,9,11,8,10,... which reproduces the sequence itself:
(1),2,(3,5),4,6,(7,9,11),8,10,12,(13,15,17,19,21),14,16,18,20,22,(23,25,27,29),24,26,28,30,(31,33,35,37,39,41),
32,34,36,38,40,42,(43,45,47,49,51,53,55),44,46,48,50,52,54,56,(57,59,61,63,65,67,69,71,73),58,60,62,64,66,68,70,72,74,
(75,77,79,81,83,85,87,89,91,93,95),76,78,80,82,84,86,88,90,92,94,96,(97,99,101,103,105,107,109,111),
98,100,102,104,106,108,110,112,(113,115,117,119,121,123,125,127,129,131),...

Mathematica

s={1, 2, 3, 5}; k=2; od={3, 5}; Do[ev=Range[od[[1]]+1, od[[-1]]+1, 2]; s=Flatten@{s, ev}; a=ev[[-1]]+1; k++; od=Range[a, a+2*s[[k]]-2, 2]; s=Flatten@{s, od}, {100}]; s

Crossrefs

Cf. A275119, A275335.

Sequence in context: A225047 A279338 A279348 * A123917 A344682 A344962

Adjacent sequences: A274497 A274498 A274499 * A274501 A274502 A274503

Keyword

nonn,base

Author

Zak Seidov and Eric Angelini, Jul 28 2016

Status

approved