

A268477


Balanced odious primes: primes with an odd number of runs of 1's in their binary expansion.


4



2, 3, 7, 31, 37, 41, 43, 53, 73, 83, 89, 101, 107, 109, 127, 137, 139, 151, 157, 163, 167, 179, 197, 211, 229, 233, 269, 281, 283, 307, 311, 313, 317, 353, 359, 367, 379, 389, 397, 401, 409, 419, 431, 433, 439, 443, 457, 461, 467, 491, 521, 523, 541, 547, 563
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OFFSET

1,1


COMMENTS

Primes from A268415.
According to our 2007conjecture, if pi_1(m) is the number of evil primes (A027699) not exceeding m and pi_2(m) is the number of odious primes (A027697) not exceeding m, then pi_1(m)<=pi_2(m) for all natural m except m=5 and m=6.
In the "balance" case of A268476,A268477, most likely, none of two types of primes
is in the majority beginning with any place.


LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10000
Vladimir Shevelev, Two analogs of ThueMorse sequence, arXiv:1603.04434 [math.NT], 2016.


MATHEMATICA

Select[Prime@ Range@ 108, OddQ@ Length[Split@ IntegerDigits[#, 2] /. {0, ___} > Nothing] &] (* Michael De Vlieger, Feb 08 2016 *)


PROG

(Python)
from sympy import prime
A268477_list = [p for p in (prime(i) for i in range(1, 10**6)) if len(list(filter(bool, format(p, 'b').split('0')))) % 2] # Chai Wah Wu, Mar 01 2016


CROSSREFS

Cf. A027697, A268415, A268476.
Sequence in context: A037151 A326358 A008840 * A156313 A163075 A265113
Adjacent sequences: A268474 A268475 A268476 * A268478 A268479 A268480


KEYWORD

nonn,base


AUTHOR

Vladimir Shevelev, Feb 05 2016


EXTENSIONS

More terms from Peter J. C. Moses, Feb 05 2016


STATUS

approved



