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

1,2

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A004038 A152038 A105614 * A116051 A124593 A125882

Adjacent sequences: A116438 A116439 A116440 * A116442 A116443 A116444

Keyword

base,nonn

Author

Giovanni Resta, Feb 15 2006

Extensions

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

Status

approved