This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A269458 #27 Feb 16 2025 08:33:30
%S A269458 3,53,61,71,89,101,107,7121,7129,7159,7187,424891,29739371,29740511,
%T A269458 29740523,29740723,1844046469,1844046481,1844046517,1844046571,
%U A269458 1844046629,1844046679,1844046733,1844046793,1844046851,1844047357,1844047421,1844047501,1845540199,1847154073,1847154109
%N A269458 Primes p such that the numbers of negabinary evil primes and negabinary odious primes not exceeding p are equal (see comment).
%C A269458 Negabinary evil and odious primes are primes in A268272 and A268273 correspondingly.
%C A269458 They are 2,5,7,13,17,19,31,37,61,67,73,79,...
%C A269458 and 3,11,23,29,41,43,47,53,59,71,83,89,...
%C A269458 In contrast to the analogous sequences 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 A269458 Vladimir Shevelev, <a href="http://arxiv.org/abs/1603.04434">Two analogs of Thue-Morse sequence</a>, arXiv:1603.04434 [math.NT], 2016.
%H A269458 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Negabinary.html">Negabinary</a>
%t A269458 aQ[n_] := EvenQ @ Total @ Rest @ Reverse @ Mod[NestWhileList[(# - Mod[#, 2])/-2 &, n, # != 0 &], 2]; s = {}; p = 2; c = 0; Do[If[aQ[p], c++, c--]; If[c == 0, AppendTo[s, p]]; p = NextPrime[p], {10^3}]; s (* _Amiram Eldar_, Sep 22 2019 after _Michael De Vlieger_ at A268272 *)
%Y A269458 Cf. A039724, A269027, A027697, A027699, A268483.
%K A269458 nonn,base
%O A269458 1,1
%A A269458 _Vladimir Shevelev_, Feb 27 2016
%E A269458 More terms from _Peter J. C. Moses_, Feb 27 2016
%E A269458 More terms from _Amiram Eldar_, Sep 22 2019