A305302 - OEIS

%I #6 May 31 2018 08:15:16

%S 1,1,2,1,2,1,3,2,2,1,2,2,4,1,3,1,2,2,5,2,2,2,4,1,4,1,2,2,4,1,2,2,2,2,

%T 4,2,6,1,3,3,2,2,5,1,4,1,3,2,4,2,5,2,2,2,6,2,4,3,7,2,2,2,4,3,2,4,8,2,

%U 4,2,4,3,6,1,2,4,4,2,6,1,2,2,4,3,6,1,2,2,4,1,2,2,4,2,4,1,4,2,4,3,6,2,4,1,2,2

%N Restricted growth sequence transform of A278222(A291760(n)), constructed from runlengths of 2-digits in base-3 representation of A254103(n).

%C For all i, j: A304746(i) = A304746(j) => a(i) = a(j).

%H Antti Karttunen, <a href="/A305302/b305302.txt">Table of n, a(n) for n = 0..65537</a>

%o (PARI)

%o A254103(n) = if(!n,n,if(!(n%2),(3*A254103(n/2))-1,(3*(1+A254103((n-1)/2)))\2));

%o A289814(n) = { my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==2, 1, 0)), 2); } \\ From A289813

%o A291760(n) = A289814(A254103(n));

%o A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };

%o A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523

%o A278222(n) = A046523(A005940(1+n));

%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 v305302 = rgs_transform(vector(65538,n,A278222(A291760(n-1))));

%o A305302(n) = v305302[1+n];

%Y Cf. A254103, A289814, A291760, A304746.

%Y Cf. also A305301, A305303.

%K nonn,base

%O 0,3

%A _Antti Karttunen_, May 30 2018