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

Author

Vladimir Shevelev, Feb 05 2016

Keywords

• nonn
• base

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.

Crossrefs

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

Programs

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 *)

Extensions

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