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

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, 10219

Offset: 1

Author

Lekraj Beedassy, Nov 08 2002

Keywords

• base
• nonn

Examples

			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.)
		

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.

Crossrefs

Cf. A072857, A077623, A076730.

Programs

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}]

Formula

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

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(54) from Giovanni Resta, Nov 06 2013