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

1,1

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

Cf. A000069, A001969, A223024, A180963.

Sequence in context: A045124 A045100 A038471 * A020150 A178389 A297304

Adjacent sequences: A224069 A224070 A224071 * A224073 A224074 A224075

Keyword

nonn,base

Author

Vladimir Shevelev, Mar 30 2013

Status

approved