A215731 -id:A215731 - cp's OEIS frontend

A217166 a(n) is the least value of k such that the decimal expansion of Lucas(k) contains n consecutive identical digits.

Original entry on oeis.org

0, 5, 36, 78, 112, 538, 3139, 6436, 17544, 82864, 328448, 1701593, 1701593, 8030342, 8030342, 77552742

Offset: 1

V. Raman, Sep 27 2012

a(12) > 1512000. - Chai Wah Wu, Dec 17 2014

a(17) > 10^8. - Nick Hobson, Feb 02 2024

Nick Hobson, C program

Cf. A000032, A045875, A215727, A215728, A215729, A215730, A215731.

C
```
// See Links section.
```

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

def A217166(n):
    if n == 1:
        return 0
    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 l:
                if k in s:
                    return m
            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 02 2024

A217190 a(n) is the number of digits in the decimal representation of the smallest power of 11 that contains n consecutive identical digits.

Original entry on oeis.org

1, 2, 9, 41, 163, 502, 1378, 3107, 9834, 41530, 223636, 308352, 308352

Offset: 1

V. Raman, Sep 27 2012

Number of digits in 11^k is equal to floor(1 + k*log_10(11)).

Cf. A215731, A215737.

k = 0; Join[{1}, Table[While[d = IntegerDigits[11^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 *)

a(10)-a(13) added by V. Raman, Apr 30 2012, in correspondence with A215731.

cp's OEIS Frontend

A217166 a(n) is the least value of k such that the decimal expansion of Lucas(k) contains n consecutive identical digits.

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