Re Base Rep Puzzle

[N. J. A. Sloane]

to round off this discussion, i am adding these 3 sequences

Neil

%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.
%D A112670 David D. 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
%O A112670 2,2
%K A112670 nonn
%Y A112670 Cf. A112671, A112672.
%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 A112671 and A112672 respectively.
%A A112670 njas, Dec 30 2005

%I A112671
%S A112671 0,1,2,4,5,7,9,11,13,16,18,21,24,27,29,32,35,39,42,45,48,52,55,58,
%T A112671 62,66,70,73,77,80,84,88,91,95,100,104,108,112,116,120,124,128,132,
%U A112671 136,141,145,149,153,158,162,166,170,175,179,183,188,193,198,202
%N A112671 Bases arising in A112670.
%O A112671 2,3
%K A112671 nonn
%A A112671 njas, Dec 30 2005

%I A112672
%S A112672 2,2,3,3,4,4,5,6,7,8,9,9,10,11,12,13,14,14,15,16,17,18,19,20,21,21,
%T A112672 22,23,24,25,26,27,28,29,29,30,31,32,33,34,35,36,37,38,38,39,40,41,
%U A112672 42,43,44,45,46,47,48,49,49,50,51,52,53,54,55,56,57,58,59,60,61,61
%N A112672 Exponents arising in A112670.
%O A112672 1,1
%K A112672 nonn
%A A112672 njas, Dec 30 2005