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URL: https://oeis.org/A045875

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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, 106892452, 356677212
OFFSET
1,2
COMMENTS
a(9) > 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
a(17) > 107000000. - Paul Geneau de Lamarlière, Feb 04 2024
MATHEMATICA
a[n_] := Block[{k = 0}, While[ !MemberQ[ Length /@ Split@ IntegerDigits[2^k], n], k++ ]; k]; Table[a[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
KEYWORD
base,nonn,hard,more
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
a(16) from Paul Geneau de Lamarlière, Feb 04 2024
a(17) from Paul Geneau de Lamarlière, Sep 24 2024
STATUS
approved