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A116438 Numbers k which when sandwiched between two 3's give a multiple of k.

%I A116438 #13 Mar 26 2023 11:15:10
%S A116438 1,3,11,13,21,33,39,77,91,137,219,411,9091,29703,909091,5882353,
%T A116438 10989011,12145749,12987013,14354067,20979021,22556391,32967033,
%U A116438 38961039,52631579,76923077,90909091,297029703,1185770751,2479338843,4347826087,9090909091,13698630137
%N A116438 Numbers k which when sandwiched between two 3's give a multiple of k.
%H A116438 Michael S. Branicky, <a href="/A116438/b116438.txt">Table of n, a(n) for n = 1..3170</a>
%e A116438 219 belongs since 32193 is a multiple of 219 (219*147).
%t A116438 f[k_, d_] := Flatten@Table[Select[Divisors[k*(10^(i + 1) + 1)], IntegerLength[ # ] == i &], {i, d}]; f[3, 10] (* _Ray Chandler_, May 11 2007 *)
%o A116438 (Python)
%o A116438 from sympy import isprime
%o A116438 from itertools import count, islice
%o A116438 def agen(): # generator of terms
%o A116438     yield from [1, 3]
%o A116438     for k in count(2):
%o A116438         t = 3*(10**(k+1) + 1)
%o A116438         yield from (t//i for i in range(300, 30, -1) if t%i == 0)
%o A116438 print(list(islice(agen(), 33))) # _Michael S. Branicky_, Mar 26 2023
%Y A116438 Cf. A116436, A116437, A116439, A116440, A116441, A116442, A116443, A116444.
%K A116438 base,nonn
%O A116438 1,2
%A A116438 _Giovanni Resta_, Feb 15 2006
%E A116438 a(31) and beyond from _Michael S. Branicky_, Mar 26 2023