A258802 Least base b >= 2 such that prime(n) is an absolute prime in base b with at least 2 distinct digits or 0 if no such base exists.

0, 0, 3, 3, 5, 4, 5, 5, 4, 4, 6, 7, 7, 7, 7, 4, 8, 8, 9, 6, 9, 9, 11, 7, 7, 9, 11, 11, 13, 10, 13, 10, 12, 11, 13, 17, 14, 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

1,3

Comments

a(n) < prime(n)-1. This is true since prime(n) in base b > prime(n) has a single digit, prime(n) in base prime(n) is written as 10 which is not an absolute prime and prime(n) in base prime(n)-1 is written as 11 which does not have 2 distinct digits.

For 1 <= n <= 10000, A258778 differs from A258802 for 50 values of n.

Conjecture: a(n) = 0 if and only if n=1 or n=2.

Links

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

Wikipedia, Permutable prime

Example

See example in A258778.

Crossrefs

Cf. A003459, A258706, A258778.

Sequence in context: A008316 A335952 A290284 * A358241 A072820 A204004

Adjacent sequences: A258799 A258800 A258801 * A258803 A258804 A258805

Keyword

nonn

Author

Chai Wah Wu, Jun 11 2015

Status

approved