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

1,2

Comments

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

Links

Table of n, a(n) for n=1..10.

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A045875.

Sequence in context: A359203 A354456 A249872 * A290356 A025030 A001554

Adjacent sequences: A238445 A238446 A238447 * A238449 A238450 A238451

Keyword

nonn,base,fini,full

Author

Derek Orr, Feb 26 2014

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

Status

approved