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

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

1,12

Comments

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

References

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

Links

Bo Gyu Jeong, Table of n, a(n) for n = 1..1000

Bo Gyu Jeong, C++ code which computes A083116 and this sequence

Prog

(Python)
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

Crossrefs

Cf. A083116, A083118.

Sequence in context: A131272 A219105 A219984 * A352467 A219001 A212945

Adjacent sequences: A083114 A083115 A083116 * A083118 A083119 A083120

Keyword

base,nonn

Author

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

Extensions

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

More terms from Bo Gyu Jeong, Jun 13 2012

Status

approved