A275119 The even integers in the sequence appear in blocks and the successive sizes of these blocks are given by the sequence itself.

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

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 a(n) for n=1..100

Index entries for sequences that are permutations of the natural numbers

Example

The blocks of even integers are indicated here by parentheses; the successive block-sizes are 1, 2, 3, 4, 6,... which reproduces the sequence itself: 1, (2), 3, (4, 6), 5, 7, (8, 10, 12), 9, 11, 13, (14, 16, 18, 20), 15, 17, 19, 21, (22, 24, 26, 28, 30, 32), 23, 25, 27, 29, 31, 33, (34, 36, 38, 40, 42), 35, 37, 39, 41, 43...

Mathematica

s={1, 2, 3, 4, 6}; k=2; ev={4, 6}; Do[od=Range[ev[[1]]+1, ev[[-1]]+1, 2]; s=Flatten@{s, od}; a=od[[-1]]+1; k++; ev=Range[a, a+2*s[[k]]-2, 2]; s=Flatten@{s, ev}, {50}]; s

Crossrefs

Sequence in context: A332807 A373038 A267106 * A218252 A080541 A330081

Adjacent sequences: A275116 A275117 A275118 * A275120 A275121 A275122

Keyword

nonn

Author

Zak Seidov and Eric Angelini, Jul 28 2016

Status

approved