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

Author

Giovanni Resta, Feb 15 2006

Keywords

• base
• nonn

Examples

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

Links

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

Crossrefs

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

Programs

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 *)

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

Extensions

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