A287224 Take all the digits of a(n) and a(n+1) then reorder them in a single integer: this will never produce a prime, no matter the rearrangement.

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

Offset

1,2

Comments

The sequence is always extended with the smallest integer not yet present that doesn't lead to a contradiction.

The sequence is infinite and might be a permutation of the integers > 0.

Links

Jean-Marc Falcoz, Table of n, a(n) for n = 1..1301

Example

The first two terms are 1 and 2 because neither 12 or 21 are primes; the next term cannot be 3 as 23 is prime; 4 is ok because neither 24 nor 42 are primes; the next term cannot be 3 as 43 is prime; etc.

Mathematica

a = {{1}}; Do[k = 1; While[Nand[! MemberQ[a, #], NoneTrue[Map[FromDigits, Permutations[a[[n - 1]]~Join~#]], PrimeQ]] &@ Set[d, IntegerDigits@ k], k++]; AppendTo[a, d], {n, 2, 83}]; FromDigits /@ a (* Michael De Vlieger, May 22 2017 *)

Crossrefs

Sequence in context: A181524 A240568 A309681 * A077867 A123124 A166236

Adjacent sequences: A287221 A287222 A287223 * A287225 A287226 A287227

Keyword

nonn,base

Author

Eric Angelini and Jean-Marc Falcoz, May 22 2017

Status

approved