

A045875


a(n) is the smallest m for which the decimal representation of 2^m contains n consecutive identical digits.


26



0, 16, 24, 41, 220, 971, 972, 8554, 42485, 42486, 271979, 1039315, 1727602, 6855865, 63416789
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OFFSET

1,2


COMMENTS

Next term is greater than 20000.  David Wasserman, Feb 16 2002
a(11) > 250000. [Robert G. Wilson v, Oct 21 2010]
a(15) > 10297974.  T. D. Noe, Sep 08 2012


LINKS

Table of n, a(n) for n=1..15.


MATHEMATICA

f[n_] := Block[{k = 0}, While[ !MemberQ[ Length /@ Split@ IntegerDigits[2^k], n], k++ ]; k]; Table[f[n], {n, 6}] (* Robert G. Wilson v, Oct 21 2010 *)


PROG

(Python)
def A045875(n):
l, x = [str(d)*n for d in range(10)], 1
for m in range(10**9):
s = str(x)
for k in l:
if k in s:
return m
x *= 2
return 'search limit reached'
# Chai Wah Wu, Dec 17 2014


CROSSREFS

Cf. A215732 (the digits).
Sequence in context: A110228 A269519 A175161 * A046434 A111046 A205187
Adjacent sequences: A045872 A045873 A045874 * A045876 A045877 A045878


KEYWORD

base,nonn,hard


AUTHOR

Erich Friedman


EXTENSIONS

More terms from David Wasserman, Feb 16 2002
a(9) and a(10) from Robert G. Wilson v, Oct 21 2010
a(11)a(13) added by T. D. Noe, Sep 04 2012
a(14) added by T. D. Noe, Sep 06 2012
Definition clarified by Daran Gill, Mar 24 2013
a(15) from Bert Dobbelaere, Feb 25 2019


STATUS

approved



