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A379126 a(1) = 1; for n > 1, a(n) is the least number k such that A325567(k) = n, or 0 if no such number exists.

%I A379126 #15 Dec 21 2024 22:29:42
%S A379126 1,4,9,8,35,18,49,16,135,70,33,36,65,98,225,32,527,270,133,140,651,66,
%T A379126 161,72,775,130,837,196,899,450,961,64,2079,1054,525,540,259,266,273,
%U A379126 280,2583,1302,129,132,2835,322,705,144,3087,1550,3213,260,3339,1674,385,392,1539,1798,3717,900,3843,1922,3969,128
%N A379126 a(1) = 1; for n > 1, a(n) is the least number k such that A325567(k) = n, or 0 if no such number exists.
%C A379126 By definition, sequence is injective (apart from possible 0's) and each a(n) is a multiple of n.
%H A379126 Antti Karttunen, <a href="/A379126/b379126.txt">Table of n, a(n) for n = 1..4096</a>
%H A379126 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A379126 <a href="/index/Ge#GF2X">Index entries for sequences operating on polynomials in ring GF(2)[X]</a>
%F A379126 a(n) = n * A379228(n).
%o A379126 (PARI)
%o A379126 A048720(b, c) = fromdigits(Vec(Pol(binary(b))*Pol(binary(c)))%2, 2);
%o A379126 A065621(n) = bitxor(n-1, n+n-1);
%o A379126 memoA325567 = Map();
%o A379126 A325567(n) = if(1==n,1,my(v); if(mapisdefined(memoA325567,n,&v), v, fordiv(n, d, if((d>1)&&A048720(A065621(n/d), d)==n, v = (n/d); break)); mapput(memoA325567,n,v); (v)));
%o A379126 A379126(n) = for(k=1,oo,if(A325567(k)==n, return(k)));
%Y A379126 Cf. A048720, A065621, A277320, A325567, A379128 (odd bisection), A379228 [= a(n)/n].
%Y A379126 Cf. also A115872, A266195, A266351.
%K A379126 nonn
%O A379126 1,2
%A A379126 _Antti Karttunen_, Dec 21 2024