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

0, 5, 25, 78, 161, 341, 1315, 28238, 56047, 283789

Offset: 1

Author

Derek Orr, Feb 26 2014

Keywords

• nonn
• base
• fini
• full

Comments

This is an increasing sequence (not necessarily strictly increasing).

Examples

			5 is the smallest exponent such that 2^5 contains two consecutive decreasing integers (2^5 = 32).
25 is the smallest exponent such that 2^25 contains three consecutive decreasing integers (2^25 = 33554432).
		

Crossrefs

Cf. A045875, A238448.

Programs

Mathematica

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 *)

Python

def StrDec(x):
  for n in range(10**5):
    count = 0
    i = 0
    if len(str(2**n)) == x and x == 1:
      return n
    while i < len(str(2**n))-1:
      if int(str(2**n)[i]) == int(str(2**n)[i+1])-1:
        count += 1
        i += 1
      else:
        if count == x-1:
          return n
        else:
          count = 0
          i += 1
    if count == x-1:
      return n
x = 1
while x < 50:
  print(StrDec(x))
  x += 1

Extensions

a(8)-a(10) from Giovanni Resta, Feb 26 2014