A101988 Number of primes (with repetition) that can be formed from digits of the n-th prime.

1, 1, 1, 1, 1, 3, 3, 1, 3, 2, 3, 4, 1, 2, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1, 3, 3, 7, 8, 3, 9, 6, 9, 11, 6, 6, 3, 7, 7, 8, 11, 10, 3, 5, 6, 10, 5, 3, 6, 4, 5, 6, 6, 4, 4, 4, 4, 3, 6, 5, 3, 6, 6, 9, 9, 8, 11, 8, 10, 8, 4, 6, 7, 7, 10, 10, 5, 6, 10, 3, 1, 6, 4, 6, 5, 4, 4, 1, 5, 4, 4, 5, 6, 3, 6, 1, 7, 5, 4, 6, 3, 5, 4

Offset: 1

Author

Zak Seidov, Jan 29 2005

Keywords

• base
• easy
• nonn

Comments

Here we put all the digits of prime(n) into a bag and ask how many not necessarily distinct primes can be formed using some or all of these digits.

Examples

			a(35)=6 because from the digits of p(35)=149, six numbers can be formed, 19, 41, 149, 419, 491 & 941, which are primes.
		

Crossrefs

Cf. A039992, A045719.

Programs

Mathematica

(* first do *) Needs["DiscreteMath`Combinatorica`"] (* then *) f[n_] := Length[ Select[ FromDigits /@ Flatten[ Permutations /@ Subsets[ IntegerDigits[ Prime[n]]], 1], PrimeQ[ # ] &] ]; Table[ f[n], {n, 102}] (* Robert G. Wilson v, Feb 10 2005 *)

Extensions

Corrected and extended by Robert G. Wilson v, Feb 10 2005

Definition clarified by Ray Chandler, Mar 01 2005