A215730 a(n) is the smallest m for which 7^m contains n consecutive identical digits.

0, 6, 31, 71, 172, 175, 1961, 6176, 33836, 61282, 305871, 856635, 2135396, 7291510, 11032874, 30775389

Offset: 1

Author

V. Raman, Aug 22 2012

Keywords

• nonn
• base
• hard

Comments

a(13) > 1116000. - Chai Wah Wu, Dec 17 2014

a(14) > 7*10^6. - Giovanni Resta, Apr 20 2016

Examples

			7^31 = 157775382034845806615042743 contains 3 consecutive identical digits.
		

Crossrefs

Cf. A215736, A045875.

Programs

Python

import sys
sys.set_int_max_str_digits(200000)
def a(n):
  st = "0123456789"
  for k in range(10**6):
    s = str(7**k)
    tot = 0
    for i in st:
      if s.count(i*n) > 0:
        tot += 1
        break
    if tot > 0:
      return k
n = 1
while n < 10:
  print(a(n), end=', ')
  n += 1
# Derek Orr, Jul 28 2014

Python

def A215730(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 *= 7
    return 'search limit reached'
# Chai Wah Wu, Dec 17 2014

Extensions

Added a(10), Rick van der Hoorn, Mar 26 2013

a(11)-a(12) from Hiroaki Yamanouchi, Aug 29 2014

a(13) from Giovanni Resta, Apr 19 2016

a(14)-a(15) from Bert Dobbelaere, Feb 15 2019

a(16) from Paul Geneau de Lamarlière, Jul 16 2024