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%I #21 Feb 11 2017 02:29:39
%S 13,43,53,139,151,193,199,223,229,239,317,397,4751,4889,4909,4937,
%T 4951,4967,5011,5023,5077,5087,5113,5297,5351,5419,6007,6053,6211,
%U 6247,6301,6317,6343,6857,9209,9421,9473,9491,10937,11047,11329,11399,11423,11443,11491
%N Primes p such that the numbers of primes not exceeding p in A268476 and A268477 are equal.
%C 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.
%H Peter J. C. Moses, <a href="/A268483/b268483.txt">Table of n, a(n) for n = 1..2000</a>
%H Vladimir Shevelev, <a href="http://arxiv.org/abs/1603.04434">Two analogs of Thue-Morse sequence</a>, arXiv:1603.04434 [math.NT], 2016.
%t 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 *)
%Y Cf. A027697, A027699, A130911, A268476, A268477.
%K nonn,base
%O 1,1
%A _Vladimir Shevelev_, Feb 05 2016
%E More terms from _Peter J. C. Moses_, Feb 05 2016