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A229826 Evil (A001969) numbers divisible by 7 but not divisible by 3.

%I A229826 #22 Feb 20 2021 07:55:38
%S A229826 77,119,154,175,238,245,287,308,329,343,350,371,413,427,455,469,476,
%T A229826 490,497,553,574,581,616,658,679,686,700,742,763,791,826,833,854,910,
%U A229826 917,931,938,952,980,994,1043,1085,1106,1127,1141,1148,1162,1169,1232,1253
%N A229826 Evil (A001969) numbers divisible by 7 but not divisible by 3.
%C A229826 By the Moser-Newman phenomenon, among the first N positive integers divisible by 3, the evil numbers are always in the majority. But what happens if we remove from the positive numbers the multiples of 3? We conjecture that in this case we obtain another phenomenon: among the first N such positive integers divisible by 7, the odious numbers (A000069) are always in the majority.
%H A229826 Harvey P. Dale, <a href="/A229826/b229826.txt">Table of n, a(n) for n = 1..1000</a>
%H A229826 J. Coquet, <a href="http://gdz.sub.uni-goettingen.de/dms/resolveppn/?PPN=GDZPPN002099551">A summation formula related to the binary digits</a>, Inventiones Mathematicae 73 (1983), pp. 107-115.
%H A229826 D. J. Newman, <a href="http://dx.doi.org/10.1090/S0002-9939-1969-0244149-8">On the number of binary digits in a multiple of three</a>, Proc. Amer. Math. Soc. 21 (1969) 719-721.
%H A229826 Vladimir Shevelev, <a href="http://www.hindawi.com/journals/ijmms/2008/908045.html">Generalized Newman phenomena and digit conjectures on primes</a>, Internat. J. of Mathematics and Math. Sciences, 2008 (2008), Article ID 908045, 1-12.
%t A229826 With[{evil=Select[Range[0,1500],EvenQ[DigitCount[#,2,1]]&]},Select[evil, Divisible[#,7]&&!Divisible[#,3]&]] (* _Harvey P. Dale_, Dec 04 2014 *)
%o A229826 (PARI) is(n)=hammingweight(n)%2==0 && gcd(n,21)==7 \\ _Charles R Greathouse IV_, Sep 30 2013
%Y A229826 Cf. A001969, A000069, A224072.
%K A229826 nonn,base
%O A229826 1,1
%A A229826 _Vladimir Shevelev_, Sep 30 2013