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 A076497 Number of primes corresponding to n-th primeval number A072857(n). 8

%I

%S 0,1,3,4,5,7,11,14,19,21,26,29,31,33,35,41,53,55,60,64,89,96,106,122,

%T 153,188,248,311,349,402,421,547,705,812,906,1098,1162,1268,1662,1738,

%U 1953,2418,2920,3133,3457,4483,4517,4917,5174,5953,6552,6799,8938,10219

%N Number of primes corresponding to n-th primeval number A072857(n).

%H Giovanni Resta, <a href="/A076497/b076497.txt">Table of n, a(n) for n = 1..100</a>

%H C. K. Caldwell, The Prime Glossary, <a href="http://primes.utm.edu/glossary/page.php?sort=Primeval">Primeval Number</a>

%H M. Keith, <a href="http://www.cadaeic.net/primeval.htm">Integers containing many embedded primes</a>

%H G. Villemin's Almanach of Numbers, <a href="http://villemin.gerard.free.fr/Wwwgvmm/Premier/primeval.htm">Nombre Primeval de Mike Keith</a>

%H Wikipedia, <a href="http://www.wikipedia.org/wiki/Primeval_number">Primeval number</a>.

%F a(n) = A039993(A072857(n)). - _M. F. Hasler_, Mar 12 2014

%e a(3) = 3 because the primeval number A072857(3) = 13 can be used to create 3 prime numbers, namely 3, 13 and 31.

%e a(6) = 7 because the primeval number A072857(7) = 113 can be used to create 7 prime numbers, namely 3, 11, 13, 31, 113, 131 and 311. (The two primes 13 and 31 can be obtained in 2 ways, therefore A075053(113) = 9.)

%t 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]]; d = -1; Do[ b = f[n]; If[b > d, Print[b]; d = b], {n, 1, 10^6}]

%Y Cf. A072857, A077623, A076730.

%K base,nonn

%O 1,3

%A _Lekraj Beedassy_, Nov 08 2002

%E Edited and extended by _Robert G. Wilson v_, Nov 12 2002

%E Links fixed by _Charles R Greathouse IV_, Aug 13 2009

%E a(40)-a(54) from _Giovanni Resta_, Nov 06 2013

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Last modified April 5 06:13 EDT 2020. Contains 333238 sequences. (Running on oeis4.)