A217192 a(n) is the number of digits in the decimal representation of the smallest Lucas number that contains n consecutive identical digits.

1, 2, 8, 17, 24, 113, 657, 1346, 3667, 17318, 68642, 355612, 355612, 1678243, 1678243, 16207565

Offset: 1

Author

V. Raman, Sep 27 2012

Keywords

• nonn
• base
• hard

Comments

Number of digits in Lucas(k) is equal to floor(1 + k*log_10((1+sqrt(5))/2)).

Crossrefs

Cf. A000032, A217166, A217176.

Programs

Mathematica

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

Python

def A217192(n):
    if n == 1:
        return 1
    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 len(s)
            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 04 2024