A268483 Primes p such that the numbers of primes not exceeding p in A268476 and A268477 are equal.

13, 43, 53, 139, 151, 193, 199, 223, 229, 239, 317, 397, 4751, 4889, 4909, 4937, 4951, 4967, 5011, 5023, 5077, 5087, 5113, 5297, 5351, 5419, 6007, 6053, 6211, 6247, 6301, 6317, 6343, 6857, 9209, 9421, 9473, 9491, 10937, 11047, 11329, 11399, 11423, 11443, 11491

Offset

1,1

Comments

In contrast to the analogous sequence for odious and evil primes (A027697, A027699), which, as we conjecture, consists of only primes 3,7,29 (see also our 2007-conjecture in A027697, A027699), here we conjecture that the sequence is infinite.

Links

Peter J. C. Moses, Table of n, a(n) for n = 1..2000

Vladimir Shevelev, Two analogs of Thue-Morse sequence, arXiv:1603.04434 [math.NT], 2016.

Mathematica

lim = 1500; s = Select[Prime@ Range@ lim, EvenQ@ Length[Split@ IntegerDigits[#, 2] /. {0, ___} -> Nothing] &]; t = Select[Prime@ Range@ lim, OddQ@ Length[Split@ IntegerDigits[#, 2] /. {0, ___} -> Nothing] &] ; Select[Prime@ Range@ lim, Count[s, p_ /; p <= #] == Count[t, q_ /; q <= #] &] (* Michael De Vlieger, Feb 08 2016 *)

Crossrefs

Cf. A027697, A027699, A130911, A268476, A268477.

Sequence in context: A129811 A108545 A136191 * A039318 A146507 A113831

Adjacent sequences: A268480 A268481 A268482 * A268484 A268485 A268486

Keyword

nonn,base

Author

Vladimir Shevelev, Feb 05 2016

Extensions

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

Status

approved