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%I #7 Jun 01 2018 21:42:17
%S 1,2,3,1,4,5,6,7,8,3,4,9,10,2,3,2,11,12,13,14,15,8,16,10,17,14,18,5,
%T 14,19,9,3,20,21,22,23,24,25,10,16,26,27,28,29,21,10,30,31,32,29,10,
%U 19,33,15,34,6,15,14,3,14,29,3,35,1,36,37,38,39,40,21,41,42,43,44,45,27,29,46,47,48,49,50,51,50,52,53,54,55,56,10,33,33,54,10,14
%N Restricted growth sequence transform of ordered pair [A278222(A305295(n)), A278222(A291763(n))], constructed from runlengths of 1-digits and 2-digits in base-3 representation of A245612(n).
%C Restricted growth sequence transform of A290093(A245612(n)).
%H Antti Karttunen, <a href="/A305433/b305433.txt">Table of n, a(n) for n = 0..65537</a>
%o (PARI)
%o A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
%o A048673(n) = (A003961(n)+1)/2;
%o A254049(n) = A048673((2*n)-1);
%o A245612(n) = if(n<2,1+n,if(!(n%2),(3*A245612(n/2))-1,A254049(A245612((n-1)/2))));
%o A289813(n) = { my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==1, 1, 0)), 2); } \\ From A289813
%o A289814(n) = { my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==2, 1, 0)), 2); } \\ From A289813
%o A305295(n) = A289813(A245612(n));
%o A291763(n) = A289814(A245612(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 Aux305433(n) = [A278222(A305295(n)), A278222(A291763(n))];
%o v305433 = rgs_transform(vector(65538,n,Aux305433(n-1)));
%o A305433(n) = v305433[1+n];
%Y Cf. A245612, A278222, A290093, A290094, A291763, A305295, A305431, A305432, A305434.
%Y Cf. also A305303.
%K nonn
%O 0,2
%A _Antti Karttunen_, Jun 01 2018
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