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%I #9 Aug 17 2012 21:39:50
%S 1,2,9,81,1024,16384,1953125,362797056,96889010407,281474976710656,
%T 150094635296999121,109418989131512359209,1000000000000000000000000,
%U 13109994191499930367061460371,19781359483314150527412524285952,442779263776840698304313192148785281
%N Smallest positive integer that has a different number of digits in each of the bases 2 through n.
%C Comment from Jack Brennan: The base of each member seems to be roughly n-O(log n*log log n). The exponent of each member seems to be roughly n*O(log n). The sequence of bases seems to only have differences of +1 or 0. The sequence of exponents seems to only have positive differences.
%C Does 120 ever appear as a base? (See A112672.)
%D David W. Wilson, Posting to Sequence Fan mailing list, Dec 28 2005
%D Jack Brennen computed the first 100 terms. Posting to Sequence Fan mailing list, Dec 28 2005
%F a(n) >> n^n. For any A < n, a(n) > exp(1/(1/log(n-A-1) - 1/log(n))). - _Charles R Greathouse IV_, May 01 2012
%e The sequence begins 2^0, 2^1, 3^2, 3^4, 4^5, 4^7, 5^9, 6^11, 7^13, 8^16, 9^18, 9^21, 10^24, 11^27, 12^29, 13^32, 14^35, 14^39, 15^42, 16^45, .... The bases and exponents are in A112672 and A112671 respectively.
%Y Cf. A112671, A112672, A112673.
%K nonn,base
%O 2,2
%A _N. J. A. Sloane_, Dec 30 2005
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