A088628 Smallest prime using all the digits of first n numbers. If necessary, extra digits can be used.

11, 127, 1123, 1423, 112543, 1124653, 1234657, 112345687, 1123465789, 10123457689, 10111123456879, 1011111223457689, 10111112233469857, 10111111122334456879, 1011111111223344557689, 10111111112233445569867

Offset: 1

Author

Amarnath Murthy, Oct 21 2003

Keywords

• base
• nonn

Comments

Conjecture: There exists a number k such that for all m > k, m not == 0 or 2 (mod 3), a(m) does not use any extra digit.

Examples

			a(5) = 112543 which is the smallest prime containing digits 1 to 5.
a(10) = 10123457689 is the smallest prime containing digits of 1,2,3,4,5,6,7,8,9 and 10.
		

Links

• Ray Chandler, Table of n, a(n) for n = 1..369 (terms < 10^1000)
• Ray Chandler, Mathematica program for A088628

Programs

Mathematica

For a(11): d = {1, 0, 1, 1, 1, 1, 1, 2, 2, 3, 4}; a = Map[ FromDigits, Join[ d, # ] & /@ Permutations[{5, 6, 7, 8, 9}]]; Min[ Select[ a, PrimeQ[ # ] & ]] (* Robert G. Wilson v, Nov 06 2003 *)
(* See above link for another program *)

Extensions

a(8) and a(9) from Robert G. Wilson v, Oct 22 2003

a(10) from Ray Chandler, Nov 01 2003

a(11) through a(16) from Robert G. Wilson v, Nov 06 2003