A276227 The successive absolute differences of the "mixed" pairs rebuild the starting sequence (see Comments for the definition of a "mixed pair").

1, 2, 3, 5, 7, 9, 4, 6, 8, 10, 12, 14, 11, 13, 17, 19, 23, 18, 15, 16, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 29, 31, 37, 41, 43, 47, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 53, 59, 61, 67, 71, 65, 58, 60, 62, 63, 64, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 73, 79, 83, 89, 97, 87, 82, 84, 85, 86, 88, 90, 91, 92

Offset

1,2

Comments

A "mixed pair" happens when a(n) and a(n+1) share exactly one prime.

The sequence starts with a(1) = 1 and is 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

Jean-Marc Falcoz, Table of n, a(n) for n = 1..4002

Index entries for sequences that are permutations of the natural numbers

Example

The "mixed pairs" are between parentheses:
(1,2),3,5,(7,9),4,6,8,10,12,(14,11),13,17,19,(23,18),15,16,20,21,22,24,25,26,27,28,30,32,33,34,35,(36,29),...
Listing the absolute differences of those parentheses gives: (1),(2),(3),(5),(7),... which is indeed the starting sequence.

Crossrefs

Sequence in context: A075012 A067090 A284173 * A355269 A274698 A139790

Adjacent sequences: A276224 A276225 A276226 * A276228 A276229 A276230

Keyword

nonn,base

Author

Eric Angelini and Jean-Marc Falcoz, Aug 29 2016

Status

approved