A268477 Balanced odious primes: primes with an odd number of runs of 1's in their binary expansion.

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

Offset

1,1

Comments

Primes from A268415.

According to our 2007-conjecture, 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 Thue-Morse 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