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

%I A116444 #14 Jan 20 2025 16:14:15
%S A116444 1,3,9,11,13,21,33,39,63,77,91,99,137,219,411,657,9091,29703,89109,
%T A116444 909091,5882353,10989011,12145749,12987013,14354067,20979021,22556391,
%U A116444 32967033,36437247,38961039,43062201,52631579,62937063,67669173,76923077,90909091,98901099
%N A116444 Numbers k which when sandwiched between two 9's give a multiple of k.
%H A116444 Michael S. Branicky, <a href="/A116444/b116444.txt">Table of n, a(n) for n = 1..5016</a>
%e A116444 411 belongs since 94119 is a multiple of 411 (411*229).
%t A116444 f[k_, d_] := Flatten@Table[Select[Divisors[k*(10^(i + 1) + 1)], IntegerLength[ # ] == i &], {i, d}]; f[9, 8] (* _Ray Chandler_, May 11 2007 *)
%t A116444 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 *)
%o A116444 (PARI) for(d=1,10,fordiv(9*10^(d+1)+9,a,if(#Str(a)==d,print1(a", ")))) /* _Martin Fuller_, May 10 2007 */
%o A116444 (Python)
%o A116444 from sympy import isprime
%o A116444 from itertools import count, islice
%o A116444 def agen(): # generator of terms
%o A116444     yield from [1, 3, 9]
%o A116444     for k in count(2):
%o A116444         t = 9*(10**(k+1) + 1)
%o A116444         yield from (t//i for i in range(900, 90, -1) if t%i == 0)
%o A116444 print(list(islice(agen(), 38))) # _Michael S. Branicky_, Mar 26 2023
%Y A116444 Cf. A116436, A116437, A116438, A116439, A116440, A116441, A116442, A116443.
%K A116444 base,nonn
%O A116444 1,2
%A A116444 _Giovanni Resta_, Feb 15 2006
%E A116444 Corrected by _Martin Fuller_, May 10 2007
%E A116444 a(35) and beyond from _Michael S. Branicky_, Mar 26 2023