A045875 a(n) is the smallest m for which the decimal representation of 2^m contains n consecutive identical digits.

0, 16, 24, 41, 220, 971, 972, 8554, 42485, 42486, 271979, 1039315, 1727602, 6855865, 63416789, 106892452

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

a(17) > 107000000. - Paul Geneau de Lamarlière, Feb 04 2024

Links

Table of n, a(n) for n=1..16.

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

Adjacent sequences: A045872 A045873 A045874 * A045876 A045877 A045878

Keyword

base,nonn,hard,more

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

a(16) from Paul Geneau de Lamarlière, Feb 04 2024

Status

approved