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

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

Offset: 1

Author

V. Raman, Sep 27 2012

Keywords

• nonn
• base
• hard

Comments

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

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

Links

• Nick Hobson, C program

Crossrefs

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

Programs

C

// See Links section.

Mathematica

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 *)

Python

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

Extensions

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

a(12)-a(16) from Nick Hobson, Feb 02 2024