A275386 The concatenation of |a(n)-a(n+1)| and a(n+1) is prime. Terms are distinct.

1, 3, 7, 9, 11, 17, 21, 23, 13, 19, 27, 29, 33, 47, 39, 41, 31, 57, 61, 37, 43, 63, 67, 53, 49, 51, 59, 69, 71, 77, 83, 79, 73, 81, 91, 87, 97, 109, 89, 101, 111, 113, 99, 1037, 121, 107, 93, 103, 123, 127, 129, 131, 119, 1023, 1031, 117, 1039, 133, 1009, 153, 157, 141, 143, 139, 137, 149, 159, 161, 151, 163, 171

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 odd integers not ending with the digit “5”.

A variant of A275602

Links

Jean-Marc Falcoz, Table of n, a(n) for n = 1..7856

Example

|1-3| = 2 and 23 is prime; |3-7| = 4 and 47 is prime; |7-9| = 2 and 29 is prime; |9-11| = 2 and 211 is prime; |11-17| = 6 and 617 is prime; etc.

Mathematica

a = {1}; Do[k = 1; While[Or[! PrimeQ@ FromDigits[IntegerDigits[Abs[a[[i - 1]] - k]]~Join~IntegerDigits[k]], MemberQ[a, k]], k++]; AppendTo[a, k], {i, 2, 71}]; a (* Michael De Vlieger, Nov 14 2016 *)

Crossrefs

cf. A275602

Sequence in context: A248667 A075607 A256465 * A275602 A173699 A287202

Adjacent sequences: A275383 A275384 A275385 * A275387 A275388 A275389

Keyword

nonn,base

Author

Eric Angelini and Jean-Marc Falcoz, Nov 14 2016

Status

approved