A258778 Least base b >= 2 such that prime(n) is an absolute prime in base b.

3, 2, 3, 2, 5, 3, 5, 5, 4, 4, 2, 7, 7, 6, 7, 4, 8, 8, 9, 6, 8, 9, 11, 7, 7, 9, 11, 11, 13, 10, 2, 10, 12, 11, 13, 17, 12, 11, 12, 9, 16, 9, 6, 13, 15, 10, 6, 11, 19, 12, 19, 13, 11, 16, 7, 17, 19, 19, 12, 7, 16, 19, 7, 10, 13, 19, 22, 7, 19, 19, 18, 18, 21, 10

Offset

1,1

Comments

a(n) < prime(n) for n > 1. This is true since prime(n) in base prime(n)-1 is written as 11 which is an absolute prime.

Conjecture: a(n) < prime(n)-1 for n > 2.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Wikipedia, Permutable prime

Example

a(78) = 13. prime(78) = 397 in base 10 and 397_10 = 247_13. Rearranging the digits in base 13, we get 274_13 = 433_10, 427_13 = 709_10, 472_13 = 769_10, 724_13 = 1213_10, 742_13 = 1237_10, all of which are prime.

Crossrefs

Cf. A003459, A258706, A258802.

Sequence in context: A165258 A238393 A092962 * A112924 A267148 A367682

Adjacent sequences: A258775 A258776 A258777 * A258779 A258780 A258781

Keyword

nonn

Author

Chai Wah Wu, Jun 11 2015

Status

approved