

A116444


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


9



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
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OFFSET

1,2


LINKS



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 *)


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)


CROSSREFS



KEYWORD

base,nonn


AUTHOR



EXTENSIONS



STATUS

approved



