A238448 Smallest number m such that 2^m contains a string of n consecutive increasing digits in its decimal representation.

0, 7, 28, 135, 391, 992, 5837, 9485, 15975, 244178

Offset: 1

Author

Derek Orr, Feb 26 2014

Keywords

• nonn
• base
• fini
• full

Comments

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

Examples

			7 is the smallest exponent such that 2^7 contains two consecutive increasing digits (2^7 = 128).
28 is the smallest exponent such that 2^28 ( = 268435456)  contains three consecutive increasing digits (456).
a(6) = 992 from  2^992 =
418558049682135672245478534789063207250548754572474065407714995457168379_345\
    678_17284890561672488119458109166910841919797858872862722356017328064756\
    15116630782786940537040715228680107267602488727296075852403533779290461\
    69580757764357779904060393635270100437362409630553424235540298930640110\
    82834640896 - _N. J. A. Sloane_, Aug 12 2018
		

Crossrefs

Cf. A045875.

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 Str(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(Str(x))
  x += 1

Extensions

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

Definition and examples corrected ("integers" changed to "digits") by N. J. A. Sloane, Aug 12 2018