A116442 Numbers n which when sandwiched between two 7's give a multiple of n.

1, 7, 11, 13, 49, 77, 91, 137, 511, 959, 9091, 69307, 909091, 5882353, 10989011, 12987013, 28340081, 33492823, 48951049, 52631579, 76923077, 90909091, 693069307, 2766798419, 4347826087, 5785123967, 9090909091, 13698630137, 51094890511, 95890410959, 909090909091

Offset

1,2

Links

Michael S. Branicky, Table of n, a(n) for n = 1..3001

Example

511 belongs since 75117 is a multiple 511 (511*147).

Mathematica

f[k_, d_] := Flatten@Table[Select[Divisors[k*(10^(i + 1) + 1)], IntegerLength[ # ] == i &], {i, d}]; f[7, 11] (* Ray Chandler, May 11 2007 *)

Prog

(Python)
from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
    yield from [1, 7]
    for k in count(2):
        t = 7*(10**(k+1) + 1)
        yield from (t//i for i in range(700, 70, -1) if t%i == 0)
print(list(islice(agen(), 32))) # Michael S. Branicky, Mar 26 2023

Crossrefs

Cf. A116436, A116437, A116438, A116439, A116440, A116441, A116443, A116444.

Sequence in context: A045460 A334092 A054299 * A191083 A288610 A062607

Adjacent sequences: A116439 A116440 A116441 * A116443 A116444 A116445

Keyword

base,nonn

Author

Giovanni Resta, Feb 15 2006

Extensions

a(29) and beyond from Michael S. Branicky, Mar 26 2023

Status

approved