A088628 - OEIS

%I #16 Jul 19 2015 01:33:22

%S 11,127,1123,1423,112543,1124653,1234657,112345687,1123465789,

%T 10123457689,10111123456879,1011111223457689,10111112233469857,

%U 10111111122334456879,1011111111223344557689,10111111112233445569867

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

%C 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.

%H Ray Chandler, <a href="/A088628/b088628.txt">Table of n, a(n) for n = 1..369</a> (terms < 10^1000)

%H Ray Chandler, <a href="/A088628/a088628.txt">Mathematica program for A088628</a>

%e a(5) = 112543 which is the smallest prime containing digits 1 to 5.

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

%t 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 *)

%t (* See above link for another program *)

%K base,nonn

%O 1,1

%A _Amarnath Murthy_, Oct 21 2003

%E a(8) and a(9) from _Robert G. Wilson v_, Oct 22 2003

%E a(10) from _Ray Chandler_, Nov 01 2003

%E a(11) through a(16) from _Robert G. Wilson v_, Nov 06 2003