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Smallest positive-integer string not explicitly embedded (in a normal left-to-right fashion) in the full decimal expansion of n^(n^n).
1

%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