

A238449


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


1




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 &]] < n1, 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 == x1:
..........return n
........else:
..........count = 0
..........i += 1
....if count == x1:
......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



