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

1,2

Comments

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

Links

Table of n, a(n) for n=1..16.

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 *)

Prog

(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

Crossrefs

Cf. A000032, A217166, A217176, A217191.

Sequence in context: A131362 A370854 A284395 * A224865 A384601 A192159

Adjacent sequences: A217189 A217190 A217191 * A217193 A217194 A217195

Keyword

nonn,base,hard,more

Author

V. Raman, Sep 27 2012

Extensions

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

a(12)-a(16) from Nick Hobson, Feb 04 2024

Status

approved