%I #25 Feb 23 2018 11:27:36
%S 1,2,3,4,4,7,12,17,20,22,25,29,46,58,63,85
%N Largest k such that there exists a decimal string of length n containing each of the first k primes as a subsequence.
%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_896.htm">Puzzle 896: Optimal packing of a set of integers</a>
%e For n=1, "2" contains the first 1 prime as a subsequence, so a(1)=1.
%e For n=2, "23" contains each of the first 2 primes as a subsequence, so a(2)=2.
%e For n=3, "235" contains each of the first 3 primes as a subsequence, so a(3)=3.
%e For n=4, "2357" contains each of the first 4 primes as a subsequence, so a(4)=4.
%e For n=5, we cannot add any new primes as the 5th prime (11) requires two extra digits, so a(5)=a(4)=4.
%e For n=6, "112357" contains each of the first 7 primes (2 to 17) as a subsequence, so a(6)=7.
%e For n=7, "1231579" contains each of the first 12 primes (2 to 37) as a subsequence, so a(7)=12.
%Y Smallest strings are in A294268.
%K nonn,base,more
%O 1,2
%A _Dmitry Kamenetsky_, Feb 11 2018