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

Author

Giovanni Resta, Feb 15 2006

Keywords

• base
• nonn

Examples

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

Links

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

Crossrefs

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

Programs

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 *)

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

Extensions

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