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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
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)
print(list(islice(agen(), 38))) # Michael S. Branicky, Mar 26 2023
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