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A369407 A variant of A008336 based on polynomials over GF(2) (see Comments for precise definition).

%I A369407 #9 Jan 24 2024 13:55:16
%S A369407 1,2,6,24,120,20,108,864,96,960,6720,624,6192,37152,491232,30702,1806,
%T A369407 127,1905,27348,486596,25102,1890,19760,456624,5581280,439712,21624,
%U A369407 451032,5199760,123954032,3966529024,123317760,3850804224,127210628096,4070965504
%N A369407 A variant of A008336 based on polynomials over GF(2) (see Comments for precise definition).
%C A369407 Let P(m) denote the polynomial over GF(2) whose coefficients are encoded in the binary expansion of the nonnegative integer m.
%C A369407 Let b(1) = 1 and for any n > 0, if P(n) divides b(n) then b(n+1) = b(n) / P(n), otherwise b(n+1) = b(n) * P(n).
%C A369407 For any n > 0, a(n) is the unique number v such that P(v) = b(n).
%H A369407 Rémy Sigrist, <a href="/A369407/b369407.txt">Table of n, a(n) for n = 1..3842</a>
%H A369407 <a href="/index/Ge#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%e A369407 The first terms, alongside the corresponding polynomials, are:
%e A369407   n   a(n)  b(n)                   P(n)
%e A369407   --  ----  ---------------------  -----------
%e A369407    1     1  1                      1
%e A369407    2     2  X                      X
%e A369407    3     6  X^2 + X                X + 1
%e A369407    4    24  X^4 + X^3              X^2
%e A369407    5   120  X^6 + X^5 + X^4 + X^3  X^2 + 1
%e A369407    6    20  X^4 + X^2              X^2 + X
%e A369407    7   108  X^6 + X^5 + X^3 + X^2  X^2 + X + 1
%e A369407    8   864  X^9 + X^8 + X^6 + X^5  X^3
%e A369407    9    96  X^6 + X^5              X^3 + 1
%e A369407   10   960  X^9 + X^8 + X^7 + X^6  X^3 + X
%o A369407 (PARI) P(n) = Mod(1, 2) * Pol(binary(n))
%o A369407 P_1(p) = fromdigits(lift(Vec(p)), 2)
%o A369407 { b = 1; for (n = 1, 36, p = P(n); if (b % p==0, b \= p, b *= p); print1 (P_1(b)", ");); }
%Y A369407 Cf. A008336.
%K A369407 nonn,base
%O A369407 1,2
%A A369407 _Rémy Sigrist_, Jan 22 2024