cp's OEIS Frontend

A141837 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 3 so that each interpretation is base 4. Terms already fully reduced (i.e., single digits) are excluded.

%I A141837 #9 Jul 21 2017 17:30:09
%S A141837 13,31,133,120332323,13023002000203
%N A141837 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 3 so that each interpretation is base 4. Terms already fully reduced (i.e., single digits) are excluded.
%C A141837 It is possible to compute additional terms by taking the last term, treating it as base-10 and converting to base-4. This will necessarily create a term 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 yields 13023002000203 as a possible next term.
%e A141837 a(3) = 133 because 133 is the first number that can produce a sequence of three terms by repeated interpretation as a base 4 number: [133] (base-4) --> [31] (base-4) --> [13] (base-4) --> [7]. Since 7 cannot be interpreted as a base 4 number, the sequence terminates with 13. a(1) = 13 because 13 is the first number that can be reduced once, yielding no further terms interpretable as base 4.
%Y A141837 Cf. A091049, A141836, A141838, A141839, A141840, A141841, A141842.
%K A141837 base,more,nonn
%O A141837 1,1
%A A141837 Chuck Seggelin (seqfan(AT)plastereddragon.com), Jul 10 2008
%E A141837 a(5) from _Giovanni Resta_, Feb 23 2013