A224072 Odd odious numbers divisible by 3.

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

Author

Vladimir Shevelev, Mar 30 2013

Keywords

• nonn
• base

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.

Crossrefs

Cf. A000069, A001969, A223024, A180963.

Programs

Mathematica

Select[Range[3, 2000, 6], OddQ[DigitCount[#, 2]][[1]] &] (* Peter J. C. Moses, Apr 04 2013 *)

PARI

isok(m) = (m % 2) && !(m % 3) && (hammingweight(m) % 2); \\ Michel Marcus, Feb 20 2021