A141842 - OEIS

%I #9 Jul 21 2017 12:41:20

%S 18,86,680,835,7087,12788,18478,128117,385732,2206280,13176873,

%T 33185141,68388408,335213686,1365888758,4771043885,24740884085

%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 8 so that each interpretation is base 9. 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 9. This may create a term minimally interpretable as base 9 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 a(15) does not produce a value minimally interpretable as base 9.

%e a(3) = 680 because 680 is the first number that can produce a sequence of three terms by repeated interpretation as a base 9 number: [680] (base-9) --> [558] (base-9) --> [458] (base-9) --> [377]. Since 377 cannot be minimally interpreted as a base 9 number, the sequence terminates with 458. a(1) = 18 because 18 is the first number that can be reduced once, yielding no further terms minimally interpretable as base 9.

%Y Cf. A091049, A141836, A141837, A141838, A141839, A141840, A141841.

%K base,more,nonn

%O 1,1

%A Chuck Seggelin (seqfan(AT)plastereddragon.com), Jul 10 2008

%E a(16)-a(17) from _Giovanni Resta_, Feb 23 2013