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A224072
Odd odious numbers divisible by 3.
4
21, 69, 81, 87, 93, 117, 171, 213, 261, 273, 279, 285, 309, 321, 327, 333, 339, 345, 351, 357, 369, 375, 381, 405, 453, 465, 471, 477, 501, 555, 597, 651, 675, 681, 687, 699, 747, 789, 837, 849, 855, 861, 885, 939, 981, 1029, 1041, 1047, 1053, 1077, 1089, 1095
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
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