cp's OEIS Frontend

A238449 Smallest numbers m such that 2^m contains a string of n consecutive decreasing integers in its decimal representation.

%I A238449 #8 May 22 2025 10:21:37
%S A238449 0,5,25,78,161,341,1315,28238,56047,283789
%N A238449 Smallest numbers m such that 2^m contains a string of n consecutive decreasing integers in its decimal representation.
%C A238449 This is an increasing sequence (not necessarily strictly increasing).
%e A238449 5 is the smallest exponent such that 2^5 contains two consecutive decreasing integers (2^5 = 32).
%e A238449 25 is the smallest exponent such that 2^25 contains three consecutive decreasing integers (2^25 = 33554432).
%t A238449 a[1] = 0; a[n_] := Block[{k = 4, p = 16}, While[Max[ Length /@  Select[ Split@ Differences@ IntegerDigits@p, First@# == -1 &]] < n-1, k++; p *= 2]; k]; a/@ Range[7] (* _Giovanni Resta_, Feb 26 2014 *)
%o A238449 (Python)
%o A238449 def StrDec(x):
%o A238449   for n in range(10**5):
%o A238449     count = 0
%o A238449     i = 0
%o A238449     if len(str(2**n)) == x and x == 1:
%o A238449       return n
%o A238449     while i < len(str(2**n))-1:
%o A238449       if int(str(2**n)[i]) == int(str(2**n)[i+1])-1:
%o A238449         count += 1
%o A238449         i += 1
%o A238449       else:
%o A238449         if count == x-1:
%o A238449           return n
%o A238449         else:
%o A238449           count = 0
%o A238449           i += 1
%o A238449     if count == x-1:
%o A238449       return n
%o A238449 x = 1
%o A238449 while x < 50:
%o A238449   print(StrDec(x))
%o A238449   x += 1
%Y A238449 Cf. A045875, A238448.
%K A238449 nonn,base,fini,full
%O A238449 1,2
%A A238449 _Derek Orr_, Feb 26 2014
%E A238449 a(8)-a(10) from _Giovanni Resta_, Feb 26 2014