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%I #16 Mar 26 2023 11:14:54
%S 1,2,3,6,11,13,14,21,22,26,33,39,42,66,77,78,91,137,146,219,274,411,
%T 438,822,9091,19802,29703,59406,909091,5882353,10989011,12145749,
%U 12987013,13986014,14354067,15037594,20979021,21978022,22556391,24291498,25974026,28708134
%N Numbers k which when sandwiched between two 6's give a multiple of k.
%H Michael S. Branicky, <a href="/A116441/b116441.txt">Table of n, a(n) for n = 1..6573</a>
%e 39 belongs to the sequence since 6396 is a multiple of 39 (39*164).
%t f[k_, d_] := Flatten@Table[Select[Divisors[k*(10^(i + 1) + 1)], IntegerLength[ # ] == i &], {i, d}]; f[6, 8] (* _Ray Chandler_, May 11 2007 *)
%t Select[Range[23000000],Divisible[FromDigits[Join[{6},IntegerDigits[#],{6}]],#]&] (* _Harvey P. Dale_, Jan 12 2011 *)
%o (Python)
%o from sympy import isprime
%o from itertools import count, islice
%o def agen(): # generator of terms
%o yield from [1, 2, 3, 6]
%o for k in count(2):
%o t = 6*(10**(k+1) + 1)
%o yield from (t//i for i in range(600, 60, -1) if t%i == 0)
%o print(list(islice(agen(), 42))) # _Michael S. Branicky_, Mar 26 2023
%Y Cf. A116436, A116437, A116438, A116439, A116440, A116442, A116443, A116444.
%K base,nonn
%O 1,2
%A _Giovanni Resta_, Feb 15 2006
%E a(40) and beyond from _Michael S. Branicky_, Mar 26 2023
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