%I A112670
%S A112670 1,2,9,81,1024,16384,1953125,362797056,96889010407,281474976710656,150094635296999121,
%T A112670 109418989131512359209,1000000000000000000000000,13109994191499930367061460371,
%U A112670 19781359483314150527412524285952,442779263776840698304313192148785281
%N A112670 Smallest positive integer that has a different number of digits in each 
               of the bases 2 through n.
%C A112670 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 A112670 Does 120 ever appear as a base? (See A112672.)
%D A112670 David W. Wilson, Posting to Sequence Fan mailing list, Dec 28 2005
%D A112670 Jack Brennen computed the first 100 terms. Posting to Sequence Fan mailing 
               list, Dec 28 2005
%e A112670 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 A112670 Cf. A112671, A112672, A112673.
%Y A112670 Sequence in context: A109519 A135868 A147302 this_sequence A117581 A123570 
               A006040
%Y A112670 Adjacent sequences: A112667 A112668 A112669 this_sequence A112671 A112672 
               A112673
%K A112670 nonn
%O A112670 2,2
%A A112670 N. J. A. Sloane (njas(AT)research.att.com), Dec 30 2005