A116443 Numbers k which when sandwiched between two 8's give a multiple of k.

1, 2, 4, 8, 11, 13, 14, 22, 26, 28, 44, 52, 56, 77, 88, 91, 137, 146, 274, 292, 548, 584, 9091, 19802, 39604, 79208, 909091, 5882353, 10989011, 12987013, 13986014, 15037594, 16194332, 19138756, 21978022, 25974026, 27972028, 30075188, 32388664, 38277512, 43956044

Offset

1,2

Links

Michael S. Branicky, Table of n, a(n) for n = 1..6504

Example

91 belongs since 8918 is a multiple of 91 (91*98 = 8918).

Mathematica

f[k_, d_] := Flatten@Table[Select[Divisors[k*(10^(i + 1) + 1)], IntegerLength[ # ] == i &], {i, d}]; f[8, 8] f[k_, d_] := Flatten@Table[Select[Divisors[k*(10^(i + 1) + 1)], IntegerLength[ # ] == i &], {i, d}]; f[9, 8] (* Ray Chandler, May 11 2007 *)
Select[Range[301*10^5], Divisible[FromDigits[Join[{8}, IntegerDigits[#], {8}]], #]&] (* Harvey P. Dale, Aug 27 2019 *)

Prog

(Python)
from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
    yield from [1, 2, 4, 8]
    for k in count(2):
        t = 8*(10**(k+1) + 1)
        yield from (t//i for i in range(800, 80, -1) if t%i == 0)
print(list(islice(agen(), 41))) # Michael S. Branicky, Mar 26 2023

Crossrefs

Cf. A116436, A116437, A116438, A116439, A116440, A116441, A116442, A116444.

Sequence in context: A136994 A137288 A247524 * A243181 A236206 A078649

Adjacent sequences: A116440 A116441 A116442 * A116444 A116445 A116446

Keyword

base,nonn

Author

Giovanni Resta, Feb 15 2006

Extensions

a(39) and beyond from Michael S. Branicky, Mar 26 2023

Status

approved