A116438 - OEIS

%I #13 Mar 26 2023 11:15:10

%S 1,3,11,13,21,33,39,77,91,137,219,411,9091,29703,909091,5882353,

%T 10989011,12145749,12987013,14354067,20979021,22556391,32967033,

%U 38961039,52631579,76923077,90909091,297029703,1185770751,2479338843,4347826087,9090909091,13698630137

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

%H Michael S. Branicky, <a href="/A116438/b116438.txt">Table of n, a(n) for n = 1..3170</a>

%e 219 belongs since 32193 is a multiple of 219 (219*147).

%t 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 (Python)

%o from sympy import isprime

%o from itertools import count, islice

%o def agen(): # generator of terms

%o     yield from [1, 3]

%o     for k in count(2):

%o         t = 3*(10**(k+1) + 1)

%o         yield from (t//i for i in range(300, 30, -1) if t%i == 0)

%o print(list(islice(agen(), 33))) # _Michael S. Branicky_, Mar 26 2023

%Y Cf. A116436, A116437, A116439, A116440, A116441, A116442, A116443, A116444.

%K base,nonn

%O 1,2

%A _Giovanni Resta_, Feb 15 2006

%E a(31) and beyond from _Michael S. Branicky_, Mar 26 2023