A217166 -id:A217166 - cp's OEIS frontend

A217176 a(n) is the first digit (from the left) to appear n times in succession in the decimal representation of the Lucas(A217166(n)).

2, 1, 3, 0, 2, 2, 9, 7, 2, 1, 1, 5, 5, 7, 7, 9

Offset: 1

V. Raman, Sep 27 2012

Cf. A000032, A215732, A215733, A215734, A215735, A215736, A215737.

k = 0; Join[{2}, Table[While[d = IntegerDigits[LucasL[k]]; prt = Partition[Differences[d], n - 1, 1]; ! MemberQ[prt, Table[0, {n - 1}]], k++]; d[[Position[prt, Table[0, {n - 1}]][[1, 1]]]], {n, 2, 8}]] (* T. D. Noe, Oct 03 2012 *)

def A217176(n):
    if n == 1:
        return 2
    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 range(10):
                if l[k] in s:
                    return k
            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 03 2024

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

Original entry on oeis.org

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

Offset: 1

V. Raman, Sep 27 2012

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

Cf. A000032, A217166, A217176.

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 *)

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

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

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

cp's OEIS Frontend

A217176 a(n) is the first digit (from the left) to appear n times in succession in the decimal representation of the Lucas(A217166(n)).

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