A215731 a(n) is the smallest m for which the decimal representation of 11^m contains n consecutive identical digits.

0, 1, 8, 39, 156, 482, 1323, 2983, 9443, 39879, 214747, 296095, 296095, 5541239, 8621384

Offset

1,3

Links

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

Example

The decimal representation of 11^39879 contains ten consecutive 6s, and is the least such power with such a string of digits.

Mathematica

mostDigits[t_] := Module[{lastDigit = t[[1]], record = 1, cnt = 1}, Do[If[t[[n]] == lastDigit, cnt++, If[cnt > record, record = cnt]; cnt = 1; lastDigit = t[[n]]], {n, 2, Length[t]}]; If[cnt > record, record = cnt] ; record]; nn = 10; t = Table[-1, {nn}]; n = -1; While[Min[t] == -1, n++; c = mostDigits[IntegerDigits[11^n]]; If[c > nn, c = nn]; While[c > 0 && t[[c]] == -1, t[[c]] = n; c--]]; t (* T. D. Noe, Apr 29 2013 *)

Prog

(Python)
def A215731(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 *= 11
    return 'search limit reached'
# Chai Wah Wu, Dec 17 2014

Crossrefs

Cf. A215737 (the repeated digits), A045875, A215727, A215728, A215729, A215730.

Sequence in context: A297017 A134415 A097787 * A144414 A045909 A264091

Adjacent sequences: A215728 A215729 A215730 * A215732 A215733 A215734

Keyword

nonn,base,more

Author

V. Raman, Aug 22 2012

Extensions

a(10) discovered by "Wick" (See http://www.mersenneforum.org/showpost.php?p=334789&postcount=89). Definition clarified and all terms to a(10) verified by Daran Gill, Mar 24 2013

a(11) discovered by Tom Womack (See http://www.mersenneforum.org/showpost.php?p=337916&postcount=105), Rick van der Hoorn, Apr 24 2013

a(12)-a(13) from Giovanni Resta, Apr 25 2013

Corrected a(12), Rick van der Hoorn, Apr 28 2013

a(14) from Giovanni Resta, Apr 18 2016

a(15) from Bert Dobbelaere, Feb 15 2019

Status

approved