%I #9 May 20 2017 21:41:16
%S 1,2,2,3,4,2,3,5,6,4,2,4,6,3,5,7,8,6,4,9,4,2,4,6,10,6,3,6,8,5,7,11,12,
%T 8,6,13,9,4,9,13,6,4,2,4,9,4,6,8,14,10,6,13,6,3,6,10,14,8,5,8,12,7,11,
%U 15,16,12,8,17,13,6,13,18,13,9,4,9,19,9,13,17,8,6,4,9,4,2,4,6,13,9,4,9,13,6,8,12,20,14,10,18,13,6,13,18,10,6,3,6,13
%N Restricted growth sequence of A278217 (prime-signature of A075159(1+n)).
%H Antti Karttunen, <a href="/A286617/b286617.txt">Table of n, a(n) for n = 0..65537</a>
%o (PARI)
%o rgs_transform(invec) = { my(occurrences = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(occurrences,invec[i]), my(pp = mapget(occurrences, invec[i])); outvec[i] = outvec[pp] , mapput(occurrences,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 A005811(n) = hammingweight(bitxor(n, n>>1)); \\ This function from _Gheorghe Coserea_, Sep 03 2015
%o A286468(n) = { my(p=((n+1)%2), i=0, m=1); while(n>0, if(((n%2)==p), m *= prime(i), p = (n%2); i = i+1); n = n\2); m };
%o A075157(n) = if(!n,n,(prime(A005811(n))*A286468(n))-1);
%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 A278217(n) = A046523(1+A075157(n));
%o write_to_bfile(0,rgs_transform(vector(65538,n,A278217(n-1))),"b286617.txt");
%Y Cf. A075159, A278217, A286539, A286619, A286622.
%K nonn,look
%O 0,2
%A _Antti Karttunen_, May 17 2017