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%I #21 Jul 31 2022 20:07:09
%S 3,153,1153,1183,3465,7673,7673,7673,65913,65913,65913,76923,232767,
%T 232767,232767,232767,232767,2307767,2307767,2307767,2307767,3076923,
%U 6923313,17078903,19507893,56695913,56695913,113322666,113322666
%N Smallest k for which k, 2*k, ..., n*k all contain the digit 3.
%C a(169) > 7*10^11. - _Giovanni Resta_, Apr 27 2017
%C a(169) = a(170) = ... = a(188) = 1538461526061, and a(189) > 2*10^12. - _David Radcliffe_, Sep 12 2018
%H Giovanni Resta, <a href="/A039934/b039934.txt">Table of n, a(n) for n = 1..168</a>
%e a(2)=153 since 153 and 306 both contain a 3, and 153 is the smallest number for which this is the case.
%o (Python)
%o from itertools import count, islice
%o def agen(startn=1, startk=1):
%o n = startn
%o for k in count(startk):
%o ki, nn = k, 0
%o while "3" in str(ki): ki += k; nn += 1
%o while n < ki//k: yield k; n += 1
%o print(list(islice(agen(), 22))) # _Michael S. Branicky_, Jul 31 2022
%Y Cf. A039932, A039933, A039935, A039936, A039937, A039938, A039939, A039940.
%K base,nonn
%O 1,1
%A _Erich Friedman_
%E More terms from _Patrick De Geest_, Oct 15 1999