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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 14 01:47 EDT 2020. Contains 336474 sequences. (Running on oeis4.)