OFFSET
1,1
COMMENTS
By Moser-Newman phenomenon among the first N positive integers multiple of 3, the evil numbers are always in the majority. Moreover, this excess tends to infinity as N goes to infinity and its growth is of order N^a, where a = log(3)/log(4).
LINKS
Peter J. C. Moses, Table of n, a(n) for n = 1..10000
J. Coquet, A summation formula related to the binary digits, Inventiones Mathematicae 73 (1983), pp. 107-115.
D. J. Newman, On the number of binary digits in a multiple of three, Proc. Amer. Math. Soc. 21 (1969) 719-721.
Vladimir Shevelev, Generalized Newman phenomena and digit conjectures on primes, Internat. J. of Mathematics and Math. Sciences, 2008 (2008), Article ID 908045, 1-12.
MATHEMATICA
Select[Range[3, 2000, 6], OddQ[DigitCount[#, 2]][[1]] &] (* Peter J. C. Moses, Apr 04 2013 *)
PROG
(PARI) isok(m) = (m % 2) && !(m % 3) && (hammingweight(m) % 2); \\ Michel Marcus, Feb 20 2021
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Vladimir Shevelev, Mar 30 2013
STATUS
approved