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%I #9 Jul 21 2017 12:41:01
%S 16,64,631,1561,4360,15466,63043,34406005,565306024,23001126626004,
%T 4562530234315632
%N 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 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 interpretable 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 interpretable as base 7.
%e a(3) = 631 because 631 is the first number that can produce a sequence of three terms by repeated interpretation as a base 7 number: [631] (base-7) --> [316] (base-7) --> [160] (base-7) --> [91]. Since 91 cannot be minimally interpreted 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 interpretable as base 7.
%Y Cf. A091049, A141836, A141837, A141838, A141839, A141841, A141842.
%K base,more,nonn
%O 1,1
%A Chuck Seggelin (seqfan(AT)plastereddragon.com), Jul 10 2008
%E a(10)-a(11) from _Giovanni Resta_, Feb 23 2013
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