A215736 -id:A215736 - cp's OEIS frontend

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

V. Raman, Aug 22 2012

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

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

			7^31 = 157775382034845806615042743 contains 3 consecutive identical digits.

Cf. A215736, A045875.

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

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

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

A217171 a(n) is the first digit (from the left) to appear six times in succession in the decimal representation n^A217161(n).

Original entry on oeis.org

8, 8, 7, 2, 1, 7, 7, 8, 0, 0, 0, 2, 4, 4, 7, 4, 6, 1, 0, 2, 9, 4, 4, 5, 9, 0, 7, 4, 0, 2, 3, 9, 4, 6, 8, 0, 3, 0, 0, 0, 6, 1, 1, 5, 3, 1, 6, 0, 0, 9, 0, 2, 7, 8, 4, 7, 6, 9, 0, 2, 5, 7, 7, 5, 9, 6, 4, 7, 0, 3, 4, 0, 4, 7, 3, 1, 2, 3, 0, 0, 0, 5, 1, 2, 3, 2, 1

Offset: 2

V. Raman, Sep 27 2012

V. Raman, Table of n, a(n) for n = 2..10000

Cf. A217161.

Cf. A215732, A215733, A215734, A215735, A215736, A215737.

Table[k = 1; While[d = IntegerDigits[n^k]; df = Partition[Differences[d], 5, 1]; ! MemberQ[df, {0, 0, 0, 0, 0}], k++]; d[[Position[df, {0, 0, 0, 0, 0}][[1, 1]]]], {n, 2, 100}] (* T. D. Noe, Oct 02 2012 *)

A217167 a(n) is the first digit (from the left) to appear two times in succession in the decimal representation of n^A217157(n).

Original entry on oeis.org

5, 7, 5, 8, 7, 1, 4, 4, 0, 1, 4, 4, 4, 2, 5, 3, 8, 9, 0, 4, 2, 8, 3, 4, 1, 4, 7, 1, 0, 8, 3, 3, 1, 2, 6, 7, 4, 4, 0, 1, 8, 8, 4, 1, 1, 2, 1, 1, 0, 7, 1, 8, 1, 5, 4, 5, 3, 1, 0, 2, 4, 0, 4, 2, 6, 4, 4, 2, 0, 1, 0, 3, 2, 7, 7, 7, 5, 0, 0, 4, 5, 8, 1, 2, 0, 3, 8

Offset: 2

V. Raman, Sep 27 2012

Note that 109^2 = 11881. So by looking at the digits from the left, we have a(109) = 1.

V. Raman, Table of n, a(n) for n = 2..10000

Cf. A217157.
Cf. A215732, A215236.
Cf. A215733, A215734, A215735, A215736, A215737.

Table[k = 1; While[d = IntegerDigits[n^k]; ! MemberQ[df = Differences[d], 0], k++]; d[[Position[df, 0][[1, 1]]]], {n, 2, 100}] (* T. D. Noe, Oct 02 2012 *)

A217168 a(n) is the first digit (from the left) to appear three times in succession in the decimal representation of n^A217158(n).

Original entry on oeis.org

7, 8, 7, 8, 7, 7, 7, 8, 0, 8, 1, 6, 1, 2, 7, 2, 2, 7, 0, 2, 8, 6, 7, 8, 4, 5, 6, 1, 0, 1, 7, 4, 7, 5, 6, 3, 4, 5, 0, 5, 1, 1, 7, 4, 5, 6, 5, 1, 0, 8, 5, 1, 1, 3, 0, 1, 0, 1, 0, 3, 8, 4, 7, 2, 9, 6, 8, 7, 0, 2, 2, 8, 2, 7, 3, 4, 5, 5, 0, 8, 7, 0, 7, 5, 2, 7, 2

Offset: 2

V. Raman, Sep 27 2012

V. Raman, Table of n, a(n) for n = 2..10000

Cf. A217158.

Cf. A215732, A215733, A215734, A215735, A215736, A215737.

Table[k = 1; While[d = IntegerDigits[n^k]; ! MemberQ[df = Partition[Differences[d], 2, 1], {0, 0}], k++]; d[[Position[df, {0, 0}][[1, 1]]]], {n, 2, 100}] (* T. D. Noe, Oct 02 2012 *)

A217169 a(n) is the first digit (from the left) to appear four times in succession in the decimal representation of n^A217159(n).

Original entry on oeis.org

5, 5, 8, 7, 0, 9, 8, 5, 0, 7, 3, 6, 1, 2, 8, 9, 5, 1, 0, 4, 4, 7, 7, 8, 2, 5, 1, 0, 0, 9, 8, 6, 5, 5, 2, 6, 5, 6, 0, 9, 6, 7, 6, 5, 1, 6, 2, 2, 0, 6, 6, 3, 3, 1, 0, 3, 1, 1, 0, 7, 6, 2, 8, 3, 5, 9, 6, 8, 0, 1, 4, 8, 6, 3, 8, 1, 7, 9, 0, 5, 6, 9, 1, 2, 8, 1, 8

Offset: 2

V. Raman, Sep 27 2012

V. Raman, Table of n, a(n) for n = 2..10000

Cf. A217159.

Cf. A215732, A215733, A215734, A215735, A215736, A215737.

Table[k = 1; While[d = IntegerDigits[n^k]; df = Partition[Differences[d], 3, 1]; ! MemberQ[df, {0, 0, 0}], k++]; d[[Position[df, {0, 0, 0}][[1, 1]]]], {n, 2, 100}] (* T. D. Noe, Oct 02 2012 *)

A217170 a(n) is the first digit (from the left) to appear five times in succession in the decimal representation of n^A217160(n).

Original entry on oeis.org

6, 5, 6, 4, 2, 5, 4, 5, 0, 6, 5, 4, 4, 1, 6, 5, 5, 9, 0, 2, 8, 6, 2, 5, 9, 2, 1, 8, 0, 2, 6, 8, 2, 6, 2, 6, 3, 8, 0, 8, 7, 0, 1, 7, 6, 3, 6, 5, 0, 6, 9, 6, 6, 9, 2, 2, 4, 4, 0, 4, 9, 4, 2, 3, 4, 4, 8, 5, 0, 2, 9, 9, 0, 9, 9, 0, 9, 6, 0, 0, 4, 9, 1, 0, 6, 1, 2

Offset: 2

V. Raman, Sep 27 2012

V. Raman, Table of n, a(n) for n = 2..10000

Cf. A217160.

Cf. A215732, A215733, A215734, A215735, A215736, A215737.

Table[k = 1; While[d = IntegerDigits[n^k]; df = Partition[Differences[d], 4, 1]; ! MemberQ[df, {0, 0, 0, 0}], k++]; d[[Position[df, {0, 0, 0, 0}][[1, 1]]]], {n, 2, 100}] (* T. D. Noe, Oct 02 2012 *)

A217172 a(n) is the first digit (from the left) to appear seven times in succession in the decimal representation of n^A217162(n).

Original entry on oeis.org

7, 2, 7, 8, 2, 3, 7, 2, 0, 6, 4, 6, 3, 2, 7, 9, 4, 9, 0, 4, 2, 4, 5, 8, 4, 2, 5, 6, 0, 2, 2, 3, 8, 7, 2, 5, 3, 0, 0, 4, 1, 9, 2, 7, 0, 8, 1, 6, 0, 4, 4, 2, 1, 2, 3, 1, 3, 4, 0, 2, 8, 8, 7, 5, 1, 7, 6, 9, 0, 4, 8, 1, 7, 5, 9, 6, 4, 3, 0, 2, 1, 1, 7, 8, 7, 8, 8

Offset: 2

V. Raman, Sep 27 2012

V. Raman, Table of n, a(n) for n = 2..1000

Cf. A217162.

Cf. A215732, A215733, A215734, A215735, A215736, A215737.

Table[k = 1; While[d = IntegerDigits[n^k]; df = Partition[Differences[d], 6, 1]; ! MemberQ[df, {0, 0, 0, 0, 0, 0}],  k++]; d[[Position[df, {0, 0, 0, 0, 0, 0}][[1, 1]]]], {n, 2, 100}] (* T. D. Noe, Oct 02 2012 *)

A217175 a(n) is the first digit (from the left) to appear n times in succession in the decimal representation of the Fibonacci(A217165(n)).

Original entry on oeis.org

0, 5, 7, 7, 1, 5, 7, 7, 3, 2, 4, 3, 4, 2, 4

Offset: 1

V. Raman, Sep 27 2012

Cf. A217165.

Cf. A000045, A215732, A215733, A215734, A215735, A215736, A215737.

k = 0; Join[{0}, Table[While[d = IntegerDigits[Fibonacci[k]]; prt = Partition[Differences[d], n - 1, 1]; ! MemberQ[prt, Table[0, {n - 1}]], k++]; d[[Position[prt, Table[0, {n - 1}]][[1, 1]]]], {n, 2, 8}]] (* T. D. Noe, Oct 03 2012 *)

def A217175(n):
    if n == 1:
        return 0
    else:
        l, y, x = [str(d)*n for d in range(10)], 0, 1
        for m in range(1, 10**9):
            s = str(x)
            for k in range(10):
                if l[k] in s:
                    return k
            y, x = x, y+x
        return 'search limit reached'
# Chai Wah Wu, Dec 17 2014

a(10)-a(11) from Chai Wah Wu, Dec 17 2014

a(12)-a(15) from Nick Hobson, Feb 14 2024

A217176 a(n) is the first digit (from the left) to appear n times in succession in the decimal representation of the Lucas(A217166(n)).

Original entry on oeis.org

2, 1, 3, 0, 2, 2, 9, 7, 2, 1, 1, 5, 5, 7, 7, 9

Offset: 1

V. Raman, Sep 27 2012

Cf. A217166.

Cf. A000032, A215732, A215733, A215734, A215735, A215736, A215737.

k = 0; Join[{2}, Table[While[d = IntegerDigits[LucasL[k]]; prt = Partition[Differences[d], n - 1, 1]; ! MemberQ[prt, Table[0, {n - 1}]], k++]; d[[Position[prt, Table[0, {n - 1}]][[1, 1]]]], {n, 2, 8}]] (* T. D. Noe, Oct 03 2012 *)

def A217176(n):
    if n == 1:
        return 2
    else:
        l, y, x = [str(d)*n for d in range(10)], 2, 1
        for m in range(1, 10**9):
            s = str(x)
            for k in range(10):
                if l[k] in s:
                    return k
            y, x = x, y+x
        return 'search limit reached'
# Chai Wah Wu, Dec 17 2014

a(11) from Chai Wah Wu, Dec 17 2014

a(12)-a(16) from Nick Hobson, Feb 03 2024

A217173 a(n) is the first digit (from the left) to appear eight times in succession in the decimal representation of n^A217163(n).

Original entry on oeis.org

1, 1, 1, 5, 7, 1, 2, 1, 0, 0, 2, 8, 3, 8, 0, 8, 8, 5, 0, 0, 5, 5, 7, 5, 4, 5, 8, 4, 0, 1, 1, 2, 7, 7, 2, 5, 5, 7, 0, 6, 8, 1, 2, 3, 6, 6, 5, 1, 0, 0, 4, 3, 5, 8, 4, 5, 3, 6, 0, 2, 9, 8, 2, 4, 1, 2, 8, 5, 0, 0, 9, 6, 8, 0, 3, 6, 4, 3, 0, 1, 0, 5, 7, 9, 7, 8, 1

Offset: 2

V. Raman, Sep 27 2012

Cf. A217163.

Cf. A215732, A215733, A215734, A215735, A215736, A215737.

Table[k = 1; While[d = IntegerDigits[n^k]; df = Partition[Differences[d], 7, 1]; ! MemberQ[df, {0, 0, 0, 0, 0, 0, 0}],  k++]; d[[Position[df, {0, 0, 0, 0, 0, 0, 0}][[1, 1]]]], {n, 2, 10}] (* T. D. Noe, Oct 02 2012 *)

cp's OEIS Frontend

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

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A217171 a(n) is the first digit (from the left) to appear six times in succession in the decimal representation n^A217161(n).

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A217167 a(n) is the first digit (from the left) to appear two times in succession in the decimal representation of n^A217157(n).

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A217168 a(n) is the first digit (from the left) to appear three times in succession in the decimal representation of n^A217158(n).

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A217169 a(n) is the first digit (from the left) to appear four times in succession in the decimal representation of n^A217159(n).

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A217170 a(n) is the first digit (from the left) to appear five times in succession in the decimal representation of n^A217160(n).

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Programs

Mathematica

A217172 a(n) is the first digit (from the left) to appear seven times in succession in the decimal representation of n^A217162(n).

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Mathematica

A217175 a(n) is the first digit (from the left) to appear n times in succession in the decimal representation of the Fibonacci(A217165(n)).

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Python

Extensions

A217176 a(n) is the first digit (from the left) to appear n times in succession in the decimal representation of the Lucas(A217166(n)).

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Keywords

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Programs

Mathematica

Python

Extensions

A217173 a(n) is the first digit (from the left) to appear eight times in succession in the decimal representation of n^A217163(n).