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

1,2

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A116436, A116437, A116439, A116440, A116441, A116442, A116443, A116444.

Sequence in context: A167612 A299974 A262433 * A191078 A281816 A117682

Adjacent sequences: A116435 A116436 A116437 * A116439 A116440 A116441

Keyword

base,nonn

Author

Giovanni Resta, Feb 15 2006

Extensions

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

Status

approved