A323235 - OEIS

%I #7 Jan 08 2019 19:08:11

%S 1,2,3,2,3,4,3,2,3,5,3,6,3,7,3,2,3,5,3,8,3,9,3,10,3,11,3,12,3,13,3,2,

%T 3,5,3,8,3,9,3,14,3,15,3,16,3,17,3,18,3,19,3,20,3,21,3,22,3,23,3,24,3,

%U 25,3,2,3,5,3,8,3,9,3,14,3,15,3,16,3,17,3,26,3,27,3,28,3,29,3,30,3,31,3,32,3,33,3,34,3,35,3,36,3,37,3,38,3

%N Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j), where f(1) = 0, f(n) = -1 if n is an odd number > 1, and f(n) = A323234(n) for even numbers >= 4.

%C For all i, j:

%C   A319701(i) = A319701(j) => a(i) = a(j),

%C   A323234(i) = A323234(j) => a(i) = a(j).

%H Antti Karttunen, <a href="/A323235/b323235.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%o (PARI)

%o up_to = 65537;

%o rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };

%o A053644(n) = { my(k=1); while(k<=n, k<<=1); (k>>1); }; \\ From A053644

%o A053645(n) = (n-A053644(n));

%o A079944off0(n) = (1==binary(2+n)[2]);

%o A323235aux(n) = if(1==n,0,if(n%2,-1,[A053645(n), A079944off0(n-2)]));

%o v323235 = rgs_transform(vector(up_to,n,A323235aux(n)));

%o A323235(n) = v323235[n];

%Y Cf. A053645, A079944, A319701, A323234.

%Y Cf. also A323241 (somewhat analogous filter sequence for prime factorization).

%K nonn

%O 1,2

%A _Antti Karttunen_, Jan 08 2019