A076449 Least number whose digits can be used to form exactly n different primes (not necessarily using all digits).

1, 2, 25, 13, 37, 107, 127, 113, 167, 1027, 179, 137, 1036, 1127, 1013, 1137, 1235, 1136, 1123, 1037, 1139, 1079, 10124, 10126, 1349, 1279, 1237, 3479, 10699, 1367, 10179, 1379, 10127, 10079, 10138, 10123, 10234, 10235, 10247, 10339, 10267

Offset: 0

Author

Lekraj Beedassy, Nov 07 2002

Keywords

• base
• nonn

Comments

Smallest m such that A039993(m) = n. - M. F. Hasler, Mar 08 2014

Mike Keith conjectures that a(n) always exists and reports that he has checked this for n <= 66. - N. J. A. Sloane, Jan 25 2008

Examples

			a(10) = 179 because 179 is the least number harboring ten primes (namely 7, 17, 19, 71, 79, 97, 179, 197, 719, 971).
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 0..2702 (terms 1..457 from Robert G. Wilson v)
• Michael S. Branicky, Python program for A076449, A072857, A076730, A134596
• C. K. Caldwell, The Prime Glossary, Primeval Number
• J. P. Delahaye, Primes Hunters, 1379 is very primeval (in French)
• Mike Keith, Integers containing many embedded primes
• W. Schneider, Primeval Numbers
• G. Villemin's Almanach of Numbers, Nombre Primeval de Mike Keith

Crossrefs

Cf. A075053, A072857 gives a similar sequence, A134596.

Programs

Mathematica

(* first do *) Needs["DiscreteMath`Combinatorica`"] (* then *) f[n_] := Length[ Select[ FromDigits /@ Flatten[ Permutations /@ Subsets[ IntegerDigits[ n]], 1], PrimeQ[ # ] &]]; t = Table[0, {50}]; Do[ a = f[n]; If[a < 50 && t[[a + 1]] == 0, t[[a + 1]] = n], {n, 12500}]; t (* Robert G. Wilson v, Feb 12 2005 *)

PARI

A076449(n)=for(m=1,oo,A039993(m)==n&&return(m)) \\ Not very efficient. - M. F. Hasler, Mar 08 2014

Python

# see linked program

Formula

a(n) = min { m | A039993(m)=n } = min A039993^{-1}(n). - M. F. Hasler, Mar 08 2014

Extensions

Edited by Robert G. Wilson v, Nov 24 2002

Keith link repaired by Charles R Greathouse IV, Aug 13 2009

Definition reworded by M. F. Hasler, Mar 08 2014

a(26) corrected by Robert G. Wilson v, Mar 12 2014