A116444 Numbers k which when sandwiched between two 9's give a multiple of k.

1, 3, 9, 11, 13, 21, 33, 39, 63, 77, 91, 99, 137, 219, 411, 657, 9091, 29703, 89109, 909091, 5882353, 10989011, 12145749, 12987013, 14354067, 20979021, 22556391, 32967033, 36437247, 38961039, 43062201, 52631579, 62937063, 67669173, 76923077, 90909091, 98901099

Offset

1,2

Links

Michael S. Branicky, Table of n, a(n) for n = 1..5016

Example

411 belongs since 94119 is a multiple of 411 (411*229).

Mathematica

f[k_, d_] := Flatten@Table[Select[Divisors[k*(10^(i + 1) + 1)], IntegerLength[ # ] == i &], {i, d}]; f[9, 8] (* Ray Chandler, May 11 2007 *)
Select[Range[10^6], Mod[FromDigits[Join[{9}, IntegerDigits[#], {9}]], #]==0&] (* The program generates the first 20 terms of the sequence. *) (* Harvey P. Dale, Jan 20 2025 *)

Prog

(PARI) for(d=1, 10, fordiv(9*10^(d+1)+9, a, if(#Str(a)==d, print1(a", ")))) /* Martin Fuller, May 10 2007 */
(Python)
from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
    yield from [1, 3, 9]
    for k in count(2):
        t = 9*(10**(k+1) + 1)
        yield from (t//i for i in range(900, 90, -1) if t%i == 0)
print(list(islice(agen(), 38))) # Michael S. Branicky, Mar 26 2023

Crossrefs

Cf. A116436, A116437, A116438, A116439, A116440, A116441, A116442, A116443.

Sequence in context: A235583 A287333 A174813 * A215820 A065136 A075720

Adjacent sequences: A116441 A116442 A116443 * A116445 A116446 A116447

Keyword

base,nonn

Author

Giovanni Resta, Feb 15 2006

Extensions

Corrected by Martin Fuller, May 10 2007

a(35) and beyond from Michael S. Branicky, Mar 26 2023

Status

approved