A269458 Primes p such that the numbers of negabinary evil primes and negabinary odious primes not exceeding p are equal (see comment).

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

Table of n, a(n) for n=1..31.

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

Cf. A039724, A269027, A027697, A027699, A268483.

Sequence in context: A364441 A143387 A228452 * A288867 A082484 A187805

Adjacent sequences: A269455 A269456 A269457 * A269459 A269460 A269461

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