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

1,2

Comments

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

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A125742 A269844 A374719 * A098720 A115091 A034924

Adjacent sequences: A116437 A116438 A116439 * A116441 A116442 A116443

Keyword

base,nonn

Author

Giovanni Resta, Feb 15 2006

Extensions

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

Status

approved