A291762 - OEIS

%I #14 Sep 11 2017 12:05:23

%S 1,2,3,4,3,5,2,6,7,5,2,8,2,9,5,10,3,8,2,8,9,9,3,11,4,9,12,13,3,14,2,

%T 15,5,5,9,16,2,9,5,11,2,17,3,13,8,5,2,18,4,13,5,13,3,11,9,19,5,5,2,20,

%U 2,9,8,21,5,14,2,8,9,17,3,22,2,9,8,13,5,14,2,18,10,9,3,23,5,5,9,19,3,20,9,8,9,9,5,24,2,13,8,25,3,14,2,19,14,5,2,22,2,17

%N Restricted growth sequence transform of ((-1)^A000120(n))*A046523(n); filter combining the parity of binary weight with the prime signature of n.

%C Equally, restricted growth sequence transform of sequence b defined as b(1) = 1; b(n) = A046523(n) + A010060(n) for n > 1, which starts as 1, 3, 2, 5, 2, 6, 3, 9, 4, 6, 3, 12, 3, 7, 6, 17, 2, 12, 3, 12, 7, 7, ...

%H Antti Karttunen, <a href="/A291762/b291762.txt">Table of n, a(n) for n = 1..65537</a>

%o (PARI)

%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 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ This function from _Charles R Greathouse IV_, Aug 17 2011

%o write_to_bfile(1,rgs_transform(vector(65537,n,((-1)^hammingweight(n))*A046523(n))),"b291762_upto65537.txt");

%o \\ Or alternatively:

%o A010060(n) = (hammingweight(n)%2);

%o f(n) = if(1==n,n,A046523(n)+A010060(n));

%o write_to_bfile(1,rgs_transform(vector(16385,n,f(n))),"b291762.txt");

%Y Cf. A000120, A010060, A046523.

%Y Cf. A101296, A286163, A291761 (related or similar filtering sequences).

%Y Cf. A027697 (positions of 2's), A027699 (of 3's), A130593 (of 5's and 7's), A230095 (of 9's).

%Y Cf. also A231431, A235001.

%K nonn

%O 1,2

%A _Antti Karttunen_, Sep 11 2017