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

1,2

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A378841 A286153 A068972 * A048867 A113626 A154539

Adjacent sequences: A116434 A116435 A116436 * A116438 A116439 A116440

Keyword

base,nonn

Author

Giovanni Resta, Feb 15 2006

Extensions

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

Status

approved