A083116 -id:A083116 - cp's OEIS frontend

A083118 Index of zeros in A083116 and A083117.

10, 16, 20, 25, 30, 32, 40, 48, 50, 60, 64, 70, 75, 80, 90, 96, 100, 110, 112, 120, 125, 128, 130, 140, 144, 150, 160, 170, 175, 176, 180, 190, 192, 200, 208, 210, 220, 224, 225, 230, 240, 250, 256, 260, 270, 272, 275, 280, 288, 290, 300, 304, 310, 320, 325, 330, 336, 340

Offset: 1

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Apr 23 2003

Numbers that do not divide a number obtained by concatenating a single digit any number of times.

Numbers divisible by either 10 or 16 or 25. - Karl-Heinz Hofmann, Nov 02 2023

Amarnath Murthy, "On the divisors of the Smarandache Unary sequence," Smarandache Notions Journal, Volume 11, 1-2-3, Spring 2000.

Karl-Heinz Hofmann, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -1).

Cf. A083116, A083117.

print([n for n in range(2,1000) if not n % 10 or not n % 16 or not n % 25])
# Karl-Heinz Hofmann, Nov 02 2023

Data section corrected and more terms from Karl-Heinz Hofmann, Nov 02 2023

A083117 Smallest k such that k*n contains a single digit with multiplicity, or 0 if no such number exists.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 37, 8547, 15873, 37, 0, 65359477124183, 37, 5847953216374269, 0, 37, 1, 48309178743961352657, 37, 0, 8547, 37, 15873, 38314176245210727969348659, 0, 3584229390681, 0, 1, 65359477124183

Offset: 1

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Apr 23 2003

a(n) = 0 if n = 10m, 16m or 25m.

Amarnath Murthy, "On the divisors of the Smarandache Unary sequence," Smarandache Notions Journal, Volume 11, 1-2-3, Spring 2000.

Bo Gyu Jeong, Table of n, a(n) for n = 1..1000
Bo Gyu Jeong, C++ code which computes A083116 and this sequence

Cf. A083116, A083118.

from itertools import count
def A083117(n):
    if not (n%10 and n%16 and n%25): return 0
    for l in count(1):
        k = (10**l-1)//9
        for a in range(1,10):
            b, c = divmod(a*k,n)
            if not c:
                return b # Chai Wah Wu, Jan 23 2024

a(21) corrected by Bo Gyu Jeong, Jun 12 2012

More terms from Bo Gyu Jeong, Jun 13 2012

cp's OEIS Frontend

A083118 Index of zeros in A083116 and A083117.

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