A116437 Numbers k which when sandwiched between two 2's give a multiple of k.

1, 2, 11, 13, 14, 22, 26, 77, 91, 137, 146, 274, 9091, 19802, 909091, 5882353, 10989011, 12987013, 13986014, 15037594, 21978022, 25974026, 52631579, 76923077, 90909091, 198019802, 1652892562, 4347826087, 8695652174, 9090909091, 13698630137, 14598540146, 27397260274

Offset: 1

Author

Giovanni Resta, Feb 15 2006

Keywords

• base
• nonn

Examples

			77 belongs since 2772 is a multiple of 77 (77*36).
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..2921

Crossrefs

Cf. A116436, A116438, A116439, A116440, A116441, A116442, A116443, A116444.

Programs

Mathematica

f[k_, d_] := Flatten@Table[Select[Divisors[k*(10^(i + 1) + 1)], IntegerLength[ # ] == i &], {i, d}]; f[2, 10] (* Ray Chandler, May 11 2007 *)

Python

from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
    yield from [1, 2]
    for k in count(2):
        t = 2*(10**(k+1) + 1)
        yield from (t//i for i in range(200, 20, -1) if t%i == 0)
print(list(islice(agen(), 33))) # Michael S. Branicky, Mar 26 2023

Extensions

a(30) and beyond from Michael S. Branicky, Mar 26 2023