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A379128 a(1) = 1; for n > 1, a(n) is the least odd number k such that A325567(k) = 2*n-1, or 0 if no such number exists.

%I A379128 #7 Dec 21 2024 22:31:55
%S A379128 1,9,35,49,135,33,65,225,527,133,651,161,775,837,899,961,2079,525,259,
%T A379128 273,2583,129,2835,705,3087,3213,3339,385,1539,3717,3843,3969,8255,
%U A379128 2077,1035,1065,9271,2325,1155,1185,4131,2573,10795,2697,11303,2821,11811,2945,12319,12573,12827,1545,13335,13589,13843,1665
%N A379128 a(1) = 1; for n > 1, a(n) is the least odd number k such that A325567(k) = 2*n-1, or 0 if no such number exists.
%H A379128 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A379128 <a href="/index/Ge#GF2X">Index entries for sequences operating on polynomials in ring GF(2)[X]</a>
%F A379128 a(n) = A379126(2*n-1).
%o A379128 (PARI)
%o A379128 A048720(b, c) = fromdigits(Vec(Pol(binary(b))*Pol(binary(c)))%2, 2);
%o A379128 A065621(n) = bitxor(n-1, n+n-1);
%o A379128 A325567(n) = if(1==n, n, fordiv(n, d, if((d>1)&&A048720(A065621(n/d), d)==n, return(n/d))));
%o A379128 memoA379127 = Map();
%o A379128 A379127(n) = if(1==n,1,my(v); if(mapisdefined(memoA379127,n,&v), v, v = A325567(2*n-1); mapput(memoA379127,n,v); (v)));
%o A379128 A379128(n) = for(k=1,oo,if(A379127(k)==(n+n-1), return(k+k-1)));
%Y A379128 Odd bisection of A379126.
%Y A379128 Cf. A048720, A065621, A277320, A325567, A379127.
%K A379128 nonn
%O A379128 1,2
%A A379128 _Antti Karttunen_, Dec 21 2024