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A238448 Smallest number m such that 2^m contains a string of n consecutive increasing digits in its decimal representation. 3
0, 7, 28, 135, 391, 992, 5837, 9485, 15975, 244178 (list; graph; refs; listen; history; text; internal format)
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: A219737 A316106 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

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Last modified September 28 21:53 EDT 2020. Contains 337414 sequences. (Running on oeis4.)