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A116439 Numbers k which when sandwiched between two 4's give a multiple of k.

%I A116439 #16 Mar 26 2023 11:15:14
%S A116439 1,2,4,11,13,14,22,26,28,44,52,77,91,137,146,274,292,548,9091,19802,
%T A116439 39604,909091,5882353,10989011,12987013,13986014,15037594,16194332,
%U A116439 19138756,21978022,25974026,27972028,30075188,43956044,51948052,52631579,76923077,90909091
%N A116439 Numbers k which when sandwiched between two 4's give a multiple of k.
%H A116439 Michael S. Branicky, <a href="/A116439/b116439.txt">Table of n, a(n) for n = 1..4735</a>
%e A116439 91 belongs since 4914 is a multiple of 91 (91*54).
%t A116439 f[k_, d_] := Flatten@Table[Select[Divisors[k*(10^(i + 1) + 1)], IntegerLength[ # ] == i &], {i, d}]; f[4, 9] (* _Ray Chandler_, May 11 2007 *)
%t A116439 Select[Range[52000000],Divisible[FromDigits[Join[{4}, IntegerDigits[#],{4}]],#]&]  (* _Harvey P. Dale_, Mar 14 2011 *)
%o A116439 (Python)
%o A116439 from sympy import isprime
%o A116439 from itertools import count, islice
%o A116439 def agen(): # generator of terms
%o A116439     yield from [1, 2, 4]
%o A116439     for k in count(2):
%o A116439         t = 4*(10**(k+1) + 1)
%o A116439         yield from (t//i for i in range(400, 40, -1) if t%i == 0)
%o A116439 print(list(islice(agen(), 38))) # _Michael S. Branicky_, Mar 26 2023
%Y A116439 Cf. A116436, A116437, A116438, A116440, A116441, A116442, A116443, A116444.
%K A116439 base,nonn
%O A116439 1,2
%A A116439 _Giovanni Resta_, Feb 15 2006
%E A116439 a(36) and beyond from _Michael S. Branicky_, Mar 26 2023