A116438 Numbers k which when sandwiched between two 3's give a multiple of k.

1, 3, 11, 13, 21, 33, 39, 77, 91, 137, 219, 411, 9091, 29703, 909091, 5882353, 10989011, 12145749, 12987013, 14354067, 20979021, 22556391, 32967033, 38961039, 52631579, 76923077, 90909091, 297029703, 1185770751, 2479338843, 4347826087, 9090909091, 13698630137

Offset: 1

Author

Giovanni Resta, Feb 15 2006

Keywords

• base
• nonn

Examples

			219 belongs since 32193 is a multiple of 219 (219*147).
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..3170

Crossrefs

Cf. A116436, A116437, 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[3, 10] (* Ray Chandler, May 11 2007 *)

Python

from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
    yield from [1, 3]
    for k in count(2):
        t = 3*(10**(k+1) + 1)
        yield from (t//i for i in range(300, 30, -1) if t%i == 0)
print(list(islice(agen(), 33))) # Michael S. Branicky, Mar 26 2023

Extensions

a(31) and beyond from Michael S. Branicky, Mar 26 2023