cp's OEIS Frontend

A382681 Conjecturally, the numbers k (not multiples of 5) such that for all x >= 0, k*2^x has a '0' in its decimal expansion.

%I A382681 #25 Jun 12 2025 00:52:17
%S A382681 7501221,7508793,10006109,10625334,12970254,15002442,15017586,
%T A382681 15685077,17975049,20012218,20752359,21250668,22500771,23501007,
%U A382681 24625029,24875024,25033207,25034183,25034771,25940508,29003907,29057504,29450021,29590047,29625044,29850293,30004884,30035172,30175941
%N A382681 Conjecturally, the numbers k (not multiples of 5) such that for all x >= 0, k*2^x has a '0' in its decimal expansion.
%C A382681 If k is a multiple of 5, then k*2^x always ends with '0' for x >= 1. We exclude these trivial cases.
%C A382681 If k is in this sequence, then so is k*2^x for all x >= 1.
%C A382681 All terms up to 30175941 have been tested up to x=10^6.
%e A382681 7501221*2^0 = 7501221 contains a '0'
%e A382681 7501221*2^1 = 15002442 contains a '0'
%e A382681 7501221*2^2 = 30004884 contains a '0'
%e A382681 7501221*2^3 = 60009768 contains a '0'
%e A382681 7501221*2^4 = 120019536 contains a '0'
%e A382681 7501221*2^5 = 240039072 contains a '0'
%e A382681 ...
%e A382681 Conjecturally, all further numbers of the form 7501221*2^k also contain '0'. Thus, 7501221 is in the sequence.
%Y A382681 Cf. A007377, A027870, A130694.
%K A382681 nonn,base
%O A382681 1,1
%A A382681 _Brian Kehrig_, Jun 02 2025