A275604 The concatenation of a(n) and |a(n)-a(n+1)| is prime and all such concatenations are different one from another. Terms are distinct.

1, 2, 5, 8, 11, 14, 23, 12, 19, 6, 7, 4, 3, 10, 9, 16, 13, 20, 31, 24, 25, 18, 17, 26, 29, 32, 15, 22, 35, 38, 41, 30, 37, 28, 27, 34, 21, 50, 39, 46, 43, 40, 49, 48, 55, 36, 53, 76, 33, 52, 51, 64, 57, 56, 47, 68, 45, 58, 65, 44, 67, 60, 59, 62, 73, 42, 61, 54, 71, 80, 63, 74, 77, 94, 75, 82, 79, 72, 83, 66

Offset

1,2

Comments

The sequence starts with a(1) = 1 and is always extended with the smallest integer not yet present that does not lead to a contradiction.

This sequence is conjectured to be a permutation of the positive integers and is a variant of A275603 that shares with it the first 174 terms.

Links

Jean-Marc Falcoz, Table of n, a(n) for n = 1..10001

Example

1,2,5,8,11,14,23,12,19,6,7,
|1-2| = 1 and 11 is prime; |2-5| = 3 and 23 is prime; |5-8| = 3 and 53 is prime; |8-11| = 3 and 83 is prime; |11-14| = 3 and 113 is prime; etc.

Mathematica

a = {1}; Do[k = 1; While[Or[! PrimeQ@ FromDigits[IntegerDigits[a[[i - 1]]]~Join~IntegerDigits[Abs[a[[i - 1]] - k]]], MemberQ[a, k]], k++]; AppendTo[a, k], {i, 2, 80}]; a (* Michael De Vlieger, Nov 14 2016 *)

Crossrefs

Cf. A275603.

Sequence in context: A287960 A102795 A275603 * A173698 A162938 A356447

Adjacent sequences: A275601 A275602 A275603 * A275605 A275606 A275607

Keyword

nonn,base

Author

Eric Angelini and Jean-Marc Falcoz, Nov 14 2016

Status

approved