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A379127 a(1) = 1; for n > 1, a(n) is the largest proper divisor d of 2n-1 such that A048720(A065621(d),(2n-1)/d) is equal to 2n-1.

%I A379127 #9 Dec 21 2024 22:29:55
%S A379127 1,1,1,1,3,1,1,1,1,1,3,1,1,1,1,1,11,5,1,1,1,1,3,1,7,1,1,1,1,1,1,1,13,
%T A379127 1,1,1,1,5,1,1,1,1,1,1,1,1,3,1,1,1,1,1,7,1,1,1,1,1,1,1,1,1,1,1,43,1,
%U A379127 19,9,1,1,1,1,1,1,1,1,3,5,1,1,23,1,11,1,1,1,1,1,1,1,1,1,1,1,3,1,1,13,1,1,1,1,1,1,1
%N A379127 a(1) = 1; for n > 1, a(n) is the largest proper divisor d of 2n-1 such that A048720(A065621(d),(2n-1)/d) is equal to 2n-1.
%C A379127 The position of the first occurrence of odd numbers k = 1, 3, 5, 7, 9, ... in this sequence is given by (1/2) * (A379128(2*k-1)+1).
%H A379127 Antti Karttunen, <a href="/A379127/b379127.txt">Table of n, a(n) for n = 1..65537</a>
%H A379127 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A379127 <a href="/index/Ge#GF2X">Index entries for sequences operating on polynomials in ring GF(2)[X]</a>
%F A379127 a(n) = A325567(2*n-1).
%o A379127 (PARI)
%o A379127 A048720(b, c) = fromdigits(Vec(Pol(binary(b))*Pol(binary(c)))%2, 2);
%o A379127 A065621(n) = bitxor(n-1, n+n-1);
%o A379127 A325567(n) = if(1==n, n, fordiv(n, d, if((d>1)&&A048720(A065621(n/d), d)==n, return(n/d))));
%o A379127 A379127(n) = A325567(2*n-1);
%Y A379127 Odd bisection of A325567.
%Y A379127 Cf. A048720, A065621, A277320, A379128.
%K A379127 nonn
%O A379127 1,5
%A A379127 _Antti Karttunen_, Dec 21 2024