A116441 Numbers k which when sandwiched between two 6's give a multiple of k.

1, 2, 3, 6, 11, 13, 14, 21, 22, 26, 33, 39, 42, 66, 77, 78, 91, 137, 146, 219, 274, 411, 438, 822, 9091, 19802, 29703, 59406, 909091, 5882353, 10989011, 12145749, 12987013, 13986014, 14354067, 15037594, 20979021, 21978022, 22556391, 24291498, 25974026, 28708134

Offset: 1

Author

Giovanni Resta, Feb 15 2006

Keywords

• base
• nonn

Examples

			39 belongs to the sequence since 6396 is a multiple of 39 (39*164).
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..6573

Crossrefs

Cf. A116436, A116437, A116438, A116439, A116440, A116442, A116443, A116444.

Programs

Mathematica

f[k_, d_] := Flatten@Table[Select[Divisors[k*(10^(i + 1) + 1)], IntegerLength[ # ] == i &], {i, d}]; f[6, 8] (* Ray Chandler, May 11 2007 *)
Select[Range[23000000],Divisible[FromDigits[Join[{6},IntegerDigits[#],{6}]],#]&]  (* Harvey P. Dale, Jan 12 2011 *)

Python

from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
    yield from [1, 2, 3, 6]
    for k in count(2):
        t = 6*(10**(k+1) + 1)
        yield from (t//i for i in range(600, 60, -1) if t%i == 0)
print(list(islice(agen(), 42))) # Michael S. Branicky, Mar 26 2023

Extensions

a(40) and beyond from Michael S. Branicky, Mar 26 2023