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Search: id:A039992
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| A039992 |
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Number of distinct primes embedded in prime p(n). |
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+0
2
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| 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; listen)
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OFFSET
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1,6
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COMMENT
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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.
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EXAMPLE
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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.
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MATHEMATICA
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Needs["DiscreteMath`Combinatorica`"]; f[n_] := Length[ Union[ Select[ FromDigits /@ Flatten[ Permutations /@ Subsets[ IntegerDigits[ Prime[n]]], 1], PrimeQ]]]; Table[f[n], {n, 102}] (from Ray Chandler and Robert G. Wilson v, Feb 25 2005)
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CROSSREFS
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a(n) = A045719(n)+1 = A039993(p(n)) A101988 gives another version.
Sequence in context: A055177 A030778 A068119 this_sequence A101988 A088420 A103585
Adjacent sequences: A039989 A039990 A039991 this_sequence A039993 A039994 A039995
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KEYWORD
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nonn,base
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AUTHOR
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Dave Wilson
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