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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

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OFFSET

2,1

COMMENTS

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

LINKS

Table of n, a(n) for n=2..67.

EXAMPLE

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.

MATHEMATICA

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

CROSSREFS