cp's OEIS Frontend

A091049 a(n) = first term which reduces to an unchanging value in n steps via repeated interpretation of a(n) as a base b+1 number where b is the largest digit of a(n).

%I A091049 #24 Jun 08 2025 16:15:42
%S A091049 1,10,15,17,18,58,72,80,88,507,683,838,1384,1807,3417,12651,18316,
%T A091049 41841,80852,132815,388315,1182482,2202048,6408851,15438855,34630248,
%U A091049 72141683,332386516,764388521,1867287828,5451218338,24187765577,68380483575,215445843883,677083325011
%N A091049 a(n) = first term which reduces to an unchanging value in n steps via repeated interpretation of a(n) as a base b+1 number where b is the largest digit of a(n).
%C A091049 There is no maximum number of steps and for any value of n, there MUST be a term a(n) that reduces in n steps. This is demonstrable as follows: take any term in the above sequence and convert it to base 2. The resulting value, if interpreted as a base 10 value will require one additional step to reduce. The resulting value may not be the FIRST value to resolve in that many steps, however, so it may not belong in this sequence.
%H A091049 Bert Dobbelaere, <a href="/A091049/b091049.txt">Table of n, a(n) for n = 0..100</a>
%H A091049 Bert Dobbelaere, <a href="/A091049/a091049.py.txt">Backtracking program (Python)</a>
%H A091049 Chuck Seggelin, <a href="https://web.archive.org/web/20040608012903/http://www.plastereddragon.com:80/maths/bases.htm">Interesting Base Conversions</a>.
%e A091049 a(0) = 1 because 1 is the first term that reduces to an unchanging value in zero steps (i.e. 1 is already fully reduced.) a(1) = 10 because 10 reduces in one step (10 in base 2 is 2, 2 does not reduce further.) a(8) = 88 because 88 reduces in 8 steps: 88 --> 80 --> 72 --> 58 --> 53 --> 33 --> 15 --> 11 --> 3.
%o A091049 (Python)
%o A091049 def A091049(n):
%o A091049     k = 1
%o A091049     while True:
%o A091049         m1 = k
%o A091049         for i in range(n+1):
%o A091049             m2 = int(str(m1),1+max(int(d) for d in str(m1)))
%o A091049             if m1 == m2:
%o A091049                 if i == n:
%o A091049                     return k
%o A091049                 else:
%o A091049                     break
%o A091049             m1 = m2
%o A091049         k += 1 # _Chai Wah Wu_, Jan 07 2015
%Y A091049 Cf. A054055 (largest digit of n) A068505 (n as base b+1 number where b=largest digit of n) A091047 (a(n) = the final value of n reached through repeated interpretation of n as a base b+1 number where b is the largest digit of n) A091048 (number of times n must be interpreted as a base b+1 number where b is the largest digit of n until an unchanging value is reached).
%K A091049 base,nonn
%O A091049 0,2
%A A091049 _Chuck Seggelin_, Dec 15 2003, Jul 09 2008
%E A091049 a(30)-a(31) from _Chai Wah Wu_, Jan 14 2015