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A039992 Number of distinct primes embedded in prime p(n). 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 5 13:26 EST 2019. Contains 329751 sequences. (Running on oeis4.)