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A238449 Smallest numbers m such that 2^m contains a string of n consecutive decreasing integers in its decimal representation. 1
0, 5, 25, 78, 161, 341, 1315, 28238, 56047, 283789 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

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

EXAMPLE

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).

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 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

CROSSREFS

Cf. A045875, A238448.

Sequence in context: A301912 A171272 A243303 * A062989 A122679 A264132

Adjacent sequences:  A238446 A238447 A238448 * A238450 A238451 A238452

KEYWORD

nonn,base,fini,full

AUTHOR

Derek Orr, Feb 26 2014

EXTENSIONS

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

STATUS

approved

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Last modified May 27 02:54 EDT 2019. Contains 323597 sequences. (Running on oeis4.)