%I #9 Mar 08 2014 10:59:18
%S 0,5,13,50,213,536,536,4582,63202,163984
%N Smallest number m such that 3^m contains a string of n consecutive decreasing integers in its decimal representation.
%e 5 is the smallest exponent such that 3^5 contains two consecutive decreasing integers (3^5 = 243).
%e 13 is the smallest exponent such that 3^13 contains three consecutive decreasing integers (3^13 = 1594323).
%o (Python)
%o def StrDec(x):
%o ..for n in range(10**5):
%o ....count = 0
%o ....i = 0
%o ....string = str(3**n)
%o ....if len(string) == x and x == 1:
%o ......return n
%o ....while i < len(string)-1:
%o ......if int(string[i]) == int(string[i+1])-1:
%o ........count += 1
%o ........i += 1
%o ......else:
%o ........if count >= x-1:
%o ..........return n
%o ........else:
%o ..........count = 0
%o ..........i += 1
%o ....if count >= x-1:
%o ......return n
%o x = 1
%o while x < 15:
%o ..print(StrDec(x))
%o ..x += 1
%Y Cf. A238449, A215727.
%K nonn,base,fini,full
%O 1,2
%A _Derek Orr_, Feb 27 2014
%E a(9)-a(10) from _Giovanni Resta_, Mar 02 2014