A215732 -id:A215732 - cp's OEIS frontend

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

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 *)

A217174 a(n) is the first digit (from the left) to appear nine times in succession in the decimal representation of n^A217164(n).

Original entry on oeis.org

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

Offset: 2

V. Raman, Sep 27 2012

Cf. A217164.

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

Table[k = 1; While[d = IntegerDigits[n^k]; df = Partition[Differences[d], 8, 1]; ! MemberQ[df, {0, 0, 0, 0, 0, 0, 0, 0}], k++]; d[[Position[df, {0, 0, 0, 0, 0, 0, 0, 0}][[1, 1]]]], {n, 2, 10}] (* T. D. Noe, Oct 02 2012 *)

A215783 The least k such that the decimal expansion of 3^k contains 9 consecutive n's.

Original entry on oeis.org

107189, 44152, 22791, 67449, 125406, 67390, 90785, 67448, 32311, 164065

Offset: 0

V. Raman, Aug 23 2012

			3^107189 = 141...2860000000000209...483 (51143 decimal digits, 0's start at position 45713).

Cf. A215727, A215732.

A217185 a(n) is the number of digits in the decimal representation of the smallest power of 2 that contains n consecutive identical digits.

Original entry on oeis.org

1, 5, 8, 13, 67, 293, 293, 2576, 12790, 12790, 81874, 312865, 520061, 2063822

Offset: 1

V. Raman, Sep 27 2012

Number of digits in 2^k is equal to floor(1 + k*log_10(2)).

Cf. A045875, A215732.

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

cp's OEIS Frontend

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

Views

Author

Keywords

Links

Crossrefs

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).

Views

Author

Keywords

Links

Crossrefs

Programs

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)).

Views

Author

Keywords

Crossrefs

Programs

Mathematica

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)).

Views

Author

Keywords

Crossrefs

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).

Views

Author

Keywords

Crossrefs

Programs

Mathematica

A217174 a(n) is the first digit (from the left) to appear nine times in succession in the decimal representation of n^A217164(n).

Views

Author

Keywords

Crossrefs

Programs

Mathematica

A215783 The least k such that the decimal expansion of 3^k contains 9 consecutive n's.

Views

Author

Keywords

Examples

Crossrefs

A217185 a(n) is the number of digits in the decimal representation of the smallest power of 2 that contains n consecutive identical digits.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica