A238449 Smallest numbers m such that 2^m contains a string of n consecutive decreasing integers in its decimal representation.

0, 5, 25, 78, 161, 341, 1315, 28238, 56047, 283789

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: A171272 A366158 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