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, 356677212

Offset: 1

Author

Erich Friedman

Keywords

• base
• nonn
• hard
• more

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

Crossrefs

Cf. A215732 (the digits).

Programs

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 *)

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

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