A045719 -id:A045719 - cp's OEIS frontend

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

David W. Wilson

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.

			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.

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

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 *)

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

Original entry on oeis.org

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

Zak Seidov, Jan 29 2005

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.

			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.

Cf. A039992, A045719.

(* 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 *)

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

Definition clarified by Ray Chandler, Mar 01 2005

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica