A217165 a(n) is the least value of k such that the decimal expansion of Fibonacci(k) contains n consecutive identical digits.

0, 10, 49, 66, 118, 883, 2202, 6493, 62334, 135241, 353587, 1162507, 5155873, 7280413, 37356153

Offset: 1

Author

V. Raman, Sep 27 2012

Keywords

• nonn
• base
• hard

Comments

a(16) > 42000000. - Paul Geneau de Lamarlière, Feb 04 2024

a(16) > 10^8. - Nick Hobson, Feb 09 2024

Links

• Nick Hobson, C program

Crossrefs

Cf. A000045, A045875, A215727, A215728, A215729, A215730, A215731.

Programs

C

// See Links section.

Mathematica

k = 0; Join[{0}, Table[While[d = IntegerDigits[Fibonacci[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 A217165(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 l:
                if k in s:
                    return m
            y, x = x, y+x
        return 'search limit reached'
# Chai Wah Wu, Dec 17 2014

Extensions

a(10)-a(11) from Chai Wah Wu, Dec 17 2014

a(12)-a(15) from Paul Geneau de Lamarlière, Feb 04 2024