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A141842 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. 6
18, 86, 680, 835, 7087, 12788, 18478, 128117, 385732, 2206280, 13176873, 33185141, 68388408, 335213686, 1365888758, 4771043885, 24740884085 (list; graph; refs; listen; history; text; internal format)



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.


Table of n, a(n) for n=1..17.


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.


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

Sequence in context: A124935 A126405 A250101 * A215191 A063788 A066854

Adjacent sequences:  A141839 A141840 A141841 * A141843 A141844 A141845




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


a(16)-a(17) from Giovanni Resta, Feb 23 2013



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Last modified December 11 15:53 EST 2018. Contains 318049 sequences. (Running on oeis4.)