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A269458
Primes p such that the numbers of negabinary evil primes and negabinary odious primes not exceeding p are equal (see comment).
0
3, 53, 61, 71, 89, 101, 107, 7121, 7129, 7159, 7187, 424891, 29739371, 29740511, 29740523, 29740723, 1844046469, 1844046481, 1844046517, 1844046571, 1844046629, 1844046679, 1844046733, 1844046793, 1844046851, 1844047357, 1844047421, 1844047501, 1845540199, 1847154073, 1847154109
OFFSET
1,1
COMMENTS
Negabinary evil and odious primes are primes in A268272 and A268273 correspondingly.
They are 2,5,7,13,17,19,31,37,61,67,73,79,...
and 3,11,23,29,41,43,47,53,59,71,83,89,...
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.
LINKS
Vladimir Shevelev, Two analogs of Thue-Morse sequence, arXiv:1603.04434 [math.NT], 2016.
Eric Weisstein's World of Mathematics, Negabinary
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Vladimir Shevelev, Feb 27 2016
EXTENSIONS
More terms from Peter J. C. Moses, Feb 27 2016
More terms from Amiram Eldar, Sep 22 2019
STATUS
approved