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A116437 Numbers k which when sandwiched between two 2's give a multiple of k.

%I A116437 #13 Mar 26 2023 11:15:06
%S A116437 1,2,11,13,14,22,26,77,91,137,146,274,9091,19802,909091,5882353,
%T A116437 10989011,12987013,13986014,15037594,21978022,25974026,52631579,
%U A116437 76923077,90909091,198019802,1652892562,4347826087,8695652174,9090909091,13698630137,14598540146,27397260274
%N A116437 Numbers k which when sandwiched between two 2's give a multiple of k.
%H A116437 Michael S. Branicky, <a href="/A116437/b116437.txt">Table of n, a(n) for n = 1..2921</a>
%e A116437 77 belongs since 2772 is a multiple of 77 (77*36).
%t A116437 f[k_, d_] := Flatten@Table[Select[Divisors[k*(10^(i + 1) + 1)], IntegerLength[ # ] == i &], {i, d}]; f[2, 10] (* _Ray Chandler_, May 11 2007 *)
%o A116437 (Python)
%o A116437 from sympy import isprime
%o A116437 from itertools import count, islice
%o A116437 def agen(): # generator of terms
%o A116437     yield from [1, 2]
%o A116437     for k in count(2):
%o A116437         t = 2*(10**(k+1) + 1)
%o A116437         yield from (t//i for i in range(200, 20, -1) if t%i == 0)
%o A116437 print(list(islice(agen(), 33))) # _Michael S. Branicky_, Mar 26 2023
%Y A116437 Cf. A116436, A116438, A116439, A116440, A116441, A116442, A116443, A116444.
%K A116437 base,nonn
%O A116437 1,2
%A A116437 _Giovanni Resta_, Feb 15 2006
%E A116437 a(30) and beyond from _Michael S. Branicky_, Mar 26 2023