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 A039993 Number of different primes embedded in n. 15
 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 3, 1, 1, 1, 3, 0, 1, 1, 1, 1, 3, 1, 2, 1, 2, 1, 2, 1, 3, 3, 1, 2, 3, 1, 4, 2, 1, 0, 1, 1, 2, 0, 1, 0, 2, 0, 0, 1, 1, 2, 3, 1, 1, 1, 2, 1, 2, 0, 1, 1, 1, 0, 1, 0, 2, 0, 0, 1, 3, 2, 4, 2, 2, 2, 1, 1, 3, 0, 0, 1, 2, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 0, 2, 0, 3, 1, 0, 0, 2, 1, 4, 2, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,13 COMMENTS a(n) counts (distinct) permuted subsequences of digits of n which denote primes. LINKS T. D. Noe, Table of n, a(n) for n=1..10000 C. K. Caldwell, The Prime Glossary, Primeval Number J. P. Delahaye, Primes Hunters, 1379 is very primeval (in French) [broken link] M. Keith, Integers containing many embedded primes W. Schneider, Primeval Numbers G. Villemin's Almanach of Numbers, Mike Keith's Primeval Number EXAMPLE a(17) = 3 since we can obtain 7, 17 and 71. a(22) = 1, since we can get only one prime (in contrast, A075053(22) = 2). a(1013) = 14 because the prime subsets derived from the digital permutations of 1013 are {3, 11, 13, 31, 101, 103, 113, 131, 311, 1013, 1031, 1103, 1301, 3011}. MATHEMATICA Needs["DiscreteMath`Combinatorica`"]; f[n_] := Block[{a = Drop[ Sort[ Subsets[ IntegerDigits[n]]], 1], b = c = {}, k = 1, l}, l = Length[a] + 1; While[k < l, b = Append[b, Permutations[ a[[k]] ]]; k++ ]; b = Union[ Flatten[b, 1]]; l = Length[b] + 1; k = 1; While[k < l, c = Append[c, FromDigits[ b[[k]] ]]; k++ ]; Count[ PrimeQ[ Union[c]], True]]; Table[ f[n], {n, 1, 105}] Table[Count[Union[FromDigits/@(Flatten[Permutations/@Subsets[ IntegerDigits[ n]], 1])], _?PrimeQ], {n, 110}] (* Harvey P. Dale, Nov 29 2017 *) PROG (PARI) A039993(n)={my(S=[], D, t, d); for(n=1, #D=vecsort(digits(n)), t=vector(n, i, 10^(i-1))~; forvec(i=vector(n, j, [1, #D]), d=vecextract(D, i); for(k=1, n!, isprime(p=vecextract(d, numtoperm(n, k))*t)&&S=setunion(S, Set(p))), 2)); #S} \\ For numbers with more than 6 digits it may be efficient to add X=[] and "#Set(i)

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Last modified May 24 20:53 EDT 2019. Contains 323534 sequences. (Running on oeis4.)