%I #10 Mar 06 2014 14:21:40
%S 0,8,20,57,332,332,6814,7926,16724,200633
%N Smallest number m such that 3^m contains a string of n consecutive increasing integers in its decimal representation.
%e 8 is the smallest exponent such that 3^8 contains two consecutive increasing integers (3^8 = 6561).
%e 20 is the smallest exponent such that 3^20 contains three consecutive increasing integers (3^20 = 3486784401).
%o (Python)
%o def StrInc(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(StrInc(x))
%o ..x += 1
%Y Cf. A238448, A215727.
%K nonn,base,fini,full
%O 1,2
%A _Derek Orr_, Feb 27 2014
%E a(8)-a(10) from _Giovanni Resta_, Mar 02 2014