%I #4 Mar 30 2012 18:39:52
%S 2,2,1,10,108,1065,10699,1000005,10000013,2
%N Smallest positive-integer string not explicitly embedded (in a normal left-to-right fashion) in the full decimal expansion of n^(n^n).
%C The ninth term, 10000013, is the smallest length-8 string not found embedded in the 369693100 digits of 9^9^9. To be rigorous, all length-7 strings (still) need to be shown to exist in the expansion.
%e 4^(4^4) contains at least one of every decimal digit, but none of its zeros is preceded by a one. Thus "10" is the smallest positive integer not embedded in the decimal form of that number.
%t Table[c = 1; While[StringPosition[ToString[i^i^i], ToString[c], 1] != {}, c++ ]; c, {i, 1, 10}]
%Y Cf. A002488.
%K nonn,base
%O 1,1
%A _Hans Havermann_, Nov 27 2003