A300825 - OEIS

%I #11 Nov 16 2019 08:16:47

%S 1,2,2,3,2,4,2,5,6,7,2,8,2,9,10,9,2,11,2,12,13,14,2,15,16,17,18,19,2,

%T 20,2,21,22,23,24,25,2,26,27,28,2,29,2,30,31,32,2,33,34,35,36,37,2,38,

%U 39,40,41,42,2,43,2,44,45,44,46,47,2,48,49,50,2,51,2,52,53,54,55,56,2,57,58,59,2,60,61,62,63,64,2,65,66,64,67,68,69

%N Filter sequence combining A300823(n) and A300824(n).

%C Restricted growth sequence transform of ordered pair [A300823(n), A300824(n)].

%C For all i, j: a(i) = a(j) => A051953(i) = A051953(j).

%H Antti Karttunen, <a href="/A300825/b300825.txt">Table of n, a(n) for n = 1..65537</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 write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }

%o A244042(n) = fromdigits(apply(x->(x%2), digits(n, 3)), 3);

%o A300823(n) = -sumdiv(n,d,(d<n)*moebius(n/d)*A244042(d));

%o A300222(n) = (n - A244042(n));

%o A300824(n) = -sumdiv(n,d,(d<n)*moebius(n/d)*A300222(d));

%o Aux300825(n) = [A300823(n), A300824(n)];

%o write_to_bfile(1,rgs_transform(vector(up_to,n,Aux300825(n))),"b300825.txt");

%Y Cf. A051953, A244042, A300222, A300823, A300824.

%Y Cf. also A293226, A300833.

%K nonn

%O 1,2

%A _Antti Karttunen_, Mar 14 2018