cp's OEIS Frontend

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.

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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).

Original entry on oeis.org

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

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Author

Vladimir Shevelev, Feb 27 2016

Keywords

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.

Crossrefs

Programs

  • 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 *)

Extensions

More terms from Peter J. C. Moses, Feb 27 2016
More terms from Amiram Eldar, Sep 22 2019
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