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

0,2

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

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

Formula

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

Example

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

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 *)

Prog

(PARI) A076449(n)=for(m=1, 9e9, A039993(m)==n&&return(n)) \\ Not very efficient. - M. F. Hasler, Mar 08 2014
(Python) # see linked program

Crossrefs

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

Sequence in context: A249634 A161575 A036502 * A153811 A101962 A092045

Adjacent sequences: A076446 A076447 A076448 * A076450 A076451 A076452

Keyword

base,nonn

Author

Lekraj Beedassy, Nov 07 2002

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

Status

approved