A039992 Number of distinct primes embedded in prime p(n).

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

Offset

1,6

Comments

a(n) counts permuted subsequences of digits of p(n) which denote primes.

We put all the digits of prime(n) into a bag and ask how many distinct primes can be formed using some or all of these digits.

Links

Table of n, a(n) for n=1..101.

Example

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.

Mathematica

Needs["DiscreteMath`Combinatorica`"]; f[n_] := Length[ Union[ Select[ FromDigits /@ Flatten[ Permutations /@ Subsets[ IntegerDigits[ Prime[n]]], 1], PrimeQ]]]; Table[f[n], {n, 102}] (* Ray Chandler and Robert G. Wilson v, Feb 25 2005 *)

Crossrefs

a(n) = A045719(n)+1 = A039993(p(n)) A101988 gives another version.

Sequence in context: A030778 A324078 A068119 * A101988 A200606 A293862

Adjacent sequences: A039989 A039990 A039991 * A039993 A039994 A039995

Keyword

nonn,base

Author

David W. Wilson

Status

approved