

A076497


Number of primes corresponding to nth primeval number A072857(n).


6



0, 1, 3, 4, 5, 7, 11, 14, 19, 21, 26, 29, 31, 33, 35, 41, 53, 55, 60, 64, 89, 96, 106, 122, 153, 188, 248, 311, 349, 402, 421, 547, 705, 812, 906, 1098, 1162, 1268, 1662, 1738, 1953, 2418, 2920, 3133, 3457, 4483, 4517, 4917, 5174, 5953, 6552, 6799, 8938
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OFFSET

1,3


LINKS

Giovanni Resta, Table of n, a(n) for n = 1..100
C. K. Caldwell, The Prime Glossary, Primeval Number
M. Keith, Integers containing many embedded primes
G. Villemin's Almanach of Numbers, Nombre Primeval de Mike Keith
Wikipedia, Primeval number.


FORMULA

a(n) = A039993(A072857(n)).  M. F. Hasler, Mar 12 2014


EXAMPLE

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


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


CROSSREFS

Cf. A072857, A077623, A076730.
Sequence in context: A101762 A139455 A095880 * A137950 A046413 A120635
Adjacent sequences: A076494 A076495 A076496 * A076498 A076499 A076500


KEYWORD

more,base,nonn


AUTHOR

Lekraj Beedassy, Nov 08 2002


EXTENSIONS

Edited and extended by Robert G. Wilson v, Nov 12 2002
Links fixed by Charles R Greathouse IV, Aug 13 2009
a(40)a(53) from Giovanni Resta, Nov 06 2013


STATUS

approved



