%I A141840
%S A141840 16,64,631,1561,4360,15466,63043,34406005,565306024
%N A141840 a(n) = first term that can be reduced in n steps via repeated interpretation 
               of a(n) as a base b+1 number where b is the largest digit of a(n), 
               such that b is always 6 so that each interpretation is base 7. Terms 
               already fully reduced (i.e. single digits) are excluded.
%C A141840 It is sometimes possible to compute additional terms by taking the last 
               term, treating it as base 10 and converting to base 7. This may create 
               a term minimally interprettable as base 7 which can converted back 
               to base 10 yielding the previous term in the sequence which will 
               itself yield N further terms. But there is no guarantee (except in 
               base 2) that the term so derived will be the first term to produce 
               a sequence of N+1 terms. There could be another, smaller, term which 
               satisfies that requirement but which uses different terms. Pushing 
               the last term of this sequence does not produce a value minimally 
               interprettable as base 7.
%e A141840 a(3) = 631 because 631 is the first number that can produce a sequence 
               of three terms by repeated interpetation as a base 7 number: [631] 
               (base-7) --> [316] (base-7) --> [160] (base-7) --> [91]. Since 91 
               cannot be minimally interpretted as a base 7 number, the sequence 
               terminates with 160. a(1) = 16 because 16 is the first number that 
               can be reduced once, yielding no further terms minimally interprettable 
               as base 7.
%Y A141840 Cf. A091049, A141836, A141837, A141838, A141839, A141841, A141842.
%Y A141840 Sequence in context: A073718 A061449 A168091 this_sequence A065404 A031446 
               A041492
%Y A141840 Adjacent sequences: A141837 A141838 A141839 this_sequence A141841 A141842 
               A141843
%K A141840 base,more,nonn
%O A141840 1,1
%A A141840 Chuck Seggelin (seqfan(AT)plastereddragon.com), Jul 10 2008