A090862 Smallest b > 10 such that the decimal representation of the n-th prime is not a prime in base b representation.

11, 11, 11, 11, 11, 12, 11, 11, 11, 12, 11, 11, 11, 14, 13, 11, 11, 11, 11, 12, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 11, 11, 12, 11, 11, 11, 11, 11, 11, 12, 12, 11, 11, 12, 11, 11, 11, 11, 11, 11, 12, 11, 11, 11, 12, 11, 11

Offset: 5

Author

Reinhard Zumkeller, Feb 12 2004

Keywords

• nonn
• base

Examples

			For n = 10: A000040(10) = 29 in base 11 2*11^1 + 9*11^0 = 31 is prime, 29 in base 12 is 2*12^1 + 9*12^0 = 33 = 3*11 is not prime, therefore a(10) = 12.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 5..10000

Crossrefs

Cf. A091922, A091923, A091924.

Programs

Mathematica

a[n_] := Module[{d = IntegerDigits[Prime[n]], b = 11}, While[PrimeQ[FromDigits[d, b]], b++]; b]; Array[a, 100, 5] (* Amiram Eldar, Mar 28 2025 *)

Formula

a(A091922(n)) = n and a(m) <> n for m < A091922(n).