A065425 Smallest odd prime greater than n such that the decimal expansion of its base n conversion is also prime.

3, 67, 5, 13, 7, 17, 11, 37, 11, 31, 13, 29, 17, 41, 17, 37, 19, 41, 23, 53, 23, 113, 31, 53, 29, 109, 29, 61, 31, 71, 41, 89, 37, 73, 37, 83, 41, 89, 41, 109, 43, 89, 47, 101, 47, 97, 61, 101, 53, 113, 53, 109, 61, 113, 59, 137, 59, 127, 61, 131, 71, 137, 67, 139, 67, 137

Offset: 2

Author

Robert G. Wilson v, Nov 15 2001

Keywords

• base
• nonn

Comments

For bases above ten, use multidigit numbers to represent the new number. See the example.

Examples

			a(15) = 41. 17d = 12, 19d = 14, 23d = 18, 29d = 114, 31d = 21 and 37d = 27, all of which are composite. But 41d = 211 which is a prime.
		

Crossrefs

Cf. A065720 - A065727.

Programs

Mathematica

Do[ k = PrimePi[n] + 1; While[ !PrimeQ[ FromDigits[ IntegerDigits[ Prime[k], n]]], k++ ]; Print[ Prime[k]], {n, 2, 50} ]

Extensions

More terms from David Wasserman, Aug 30 2002