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A116440 Numbers k which when sandwiched between two 5's give a multiple of k.

%I A116440 #19 Mar 26 2023 11:15:02
%S A116440 1,5,11,13,35,55,65,77,91,137,365,685,9091,49505,909091,5882353,
%T A116440 10989011,12987013,20242915,23923445,34965035,37593985,52631579,
%U A116440 54945055,64935065,76923077,90909091,495049505,1976284585,4132231405,4347826087,9090909091,13698630137
%N A116440 Numbers k which when sandwiched between two 5's give a multiple of k.
%C A116440 All terms must be odd. - _Harvey P. Dale_, Jul 29 2015
%H A116440 Michael S. Branicky, <a href="/A116440/b116440.txt">Table of n, a(n) for n = 1..3294</a>
%e A116440 137 belongs since 51375 is a multiple 137 (137*375).
%p A116440 a:=proc(n) local nn: nn:=convert(n,base,10): if type((5+10*n+5*10^(nops(nn)+1))/n, integer)=true then n else fi end: seq(a(n),n=1..10000); # _Emeric Deutsch_, Feb 28 2006
%t A116440 f[k_, d_] := Flatten@Table[Select[Divisors[k*(10^(i + 1) + 1)], IntegerLength[ # ] == i &], {i, d}]; f[5, 10] (* _Ray Chandler_, May 11 2007 *)
%o A116440 (Python)
%o A116440 from sympy import isprime
%o A116440 from itertools import count, islice
%o A116440 def agen(): # generator of terms
%o A116440     yield from [1, 5]
%o A116440     for k in count(2):
%o A116440         t = 5*(10**(k+1) + 1)
%o A116440         yield from (t//i for i in range(500, 50, -1) if t%i == 0)
%o A116440 print(list(islice(agen(), 33))) # _Michael S. Branicky_, Mar 26 2023
%Y A116440 Cf. A116436, A116437, A116438, A116439, A116441, A116442, A116443, A116444.
%K A116440 base,nonn
%O A116440 1,2
%A A116440 _Giovanni Resta_, Feb 15 2006
%E A116440 a(31) and beyond from _Michael S. Branicky_, Mar 26 2023