%I #45 Nov 09 2024 14:38:54
%S 0,6,31,71,172,175,1961,6176,33836,61282,305871,856635,2135396,
%T 7291510,11032874,30775389
%N a(n) is the smallest m for which 7^m contains n consecutive identical digits.
%C a(13) > 1116000. - _Chai Wah Wu_, Dec 17 2014
%C a(14) > 7*10^6. - _Giovanni Resta_, Apr 20 2016
%e 7^31 = 157775382034845806615042743 contains 3 consecutive identical digits.
%o (Python)
%o import sys
%o sys.set_int_max_str_digits(200000)
%o def a(n):
%o st = "0123456789"
%o for k in range(10**6):
%o s = str(7**k)
%o tot = 0
%o for i in st:
%o if s.count(i*n) > 0:
%o tot += 1
%o break
%o if tot > 0:
%o return k
%o n = 1
%o while n < 10:
%o print(a(n), end=', ')
%o n += 1
%o # _Derek Orr_, Jul 28 2014
%o (Python)
%o def A215730(n):
%o l, x = [str(d)*n for d in range(10)], 1
%o for m in range(10**9):
%o s = str(x)
%o for k in l:
%o if k in s:
%o return m
%o x *= 7
%o return 'search limit reached'
%o # _Chai Wah Wu_, Dec 17 2014
%Y Cf. A215736, A045875.
%K nonn,base,hard,changed
%O 1,2
%A _V. Raman_, Aug 22 2012
%E Added a(10), _Rick van der Hoorn_, Mar 26 2013
%E a(11)-a(12) from _Hiroaki Yamanouchi_, Aug 29 2014
%E a(13) from _Giovanni Resta_, Apr 19 2016
%E a(14)-a(15) from _Bert Dobbelaere_, Feb 15 2019
%E a(16) from _Paul Geneau de Lamarlière_, Jul 16 2024