A116440 Numbers k which when sandwiched between two 5's give a multiple of k.

1, 5, 11, 13, 35, 55, 65, 77, 91, 137, 365, 685, 9091, 49505, 909091, 5882353, 10989011, 12987013, 20242915, 23923445, 34965035, 37593985, 52631579, 54945055, 64935065, 76923077, 90909091, 495049505, 1976284585, 4132231405, 4347826087, 9090909091, 13698630137

Offset: 1

Author

Giovanni Resta, Feb 15 2006

Keywords

• base
• nonn

Comments

All terms must be odd. - Harvey P. Dale, Jul 29 2015

Examples

			137 belongs since 51375 is a multiple 137 (137*375).
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..3294

Crossrefs

Cf. A116436, A116437, A116438, A116439, A116441, A116442, A116443, A116444.

Programs

Maple

a:=proc(n) local nn: nn:=convert(n,base,10): if type((5+10*n+5*10^(nops(nn)+1))/n, integer)=true then n else fi end: seq(a(n),n=1..10000); # Emeric Deutsch, Feb 28 2006

Mathematica

f[k_, d_] := Flatten@Table[Select[Divisors[k*(10^(i + 1) + 1)], IntegerLength[ # ] == i &], {i, d}]; f[5, 10] (* Ray Chandler, May 11 2007 *)

Python

from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
    yield from [1, 5]
    for k in count(2):
        t = 5*(10**(k+1) + 1)
        yield from (t//i for i in range(500, 50, -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