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 A369318 #8 Jan 21 2024 09:37:32 %S A369318 5,9,17,23,27,29,33,35,39,45,53,57,65,71,77,83,85,89,95,101,105,107, %T A369318 113,119,125,129,135,139,141,149,153,159,165,169,177,179,183,189,195, %U A369318 197,201,209,215,221,223,225,231,237,245,249,251,257,259,263,269,277 %N A369318 Numbers k such that A091255(k, k + 1) <> 1. %C A369318 Equivalently, numbers k such that A369317(k) <> 1. %C A369318 Two consecutive integers are always coprime, however the polynomials over GF(2) whose coefficients are encoded in the binary expansions of two consecutive integers are not necessarily coprime, hence this sequence. %H A369318 <a href="/index/Ge#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a> %e A369318 The first terms, alongside the correspond GF(2)[X]-polynomials, are: %e A369318 n a(n) P(a(n)) P(a(n)+1) gcd(P(a(n)), P(a(n)+1)) %e A369318 -- ---- ------------------- ------------------- ----------------------- %e A369318 1 5 X^2 + 1 X^2 + X X + 1 %e A369318 2 9 X^3 + 1 X^3 + X X + 1 %e A369318 3 17 X^4 + 1 X^4 + X X + 1 %e A369318 4 23 X^4 + X^2 + X + 1 X^4 + X^3 X + 1 %e A369318 5 27 X^4 + X^3 + X + 1 X^4 + X^3 + X^2 X^2 + X + 1 %e A369318 6 29 X^4 + X^3 + X^2 + 1 X^4 + X^3 + X^2 + X X + 1 %e A369318 7 33 X^5 + 1 X^5 + X X + 1 %e A369318 8 35 X^5 + X + 1 X^5 + X^2 X^2 + X + 1 %e A369318 9 39 X^5 + X^2 + X + 1 X^5 + X^3 X^2 + 1 %e A369318 10 45 X^5 + X^3 + X^2 + 1 X^5 + X^3 + X^2 + X X + 1 %o A369318 (PARI) is(n) = fromdigits(lift(Vec(gcd(Mod(1, 2) * Pol(binary(n)), Mod(1, 2) * Pol(binary(n+1))))), 2) != 1 %Y A369318 Cf. A091255, A369317. %K A369318 nonn,base %O A369318 1,1 %A A369318 _Rémy Sigrist_, Jan 19 2024