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A305432 Restricted growth sequence transform of A278222(A291763(n)), constructed from runlengths of 2-digits in base-3 representation of A245612(n).

%I A305432 #5 Jun 01 2018 21:42:09
%S A305432 1,2,2,1,2,1,3,1,2,2,2,3,4,2,2,2,2,4,5,2,2,2,6,4,4,2,7,1,2,1,3,2,2,6,
%T A305432 8,3,9,2,4,6,2,4,3,4,6,4,8,1,4,4,4,1,6,2,3,3,2,2,2,2,4,2,4,1,2,2,9,8,
%U A305432 8,6,6,1,9,10,6,4,4,4,11,2,2,2,8,2,4,7,8,2,6,4,6,6,8,4,2,2,4,1,6,9,4,6,12,2,6,7
%N A305432 Restricted growth sequence transform of A278222(A291763(n)), constructed from runlengths of 2-digits in base-3 representation of A245612(n).
%H A305432 Antti Karttunen, <a href="/A305432/b305432.txt">Table of n, a(n) for n = 0..65537</a>
%o A305432 (PARI)
%o A305432 A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
%o A305432 A048673(n) = (A003961(n)+1)/2;
%o A305432 A254049(n) = A048673((2*n)-1);
%o A305432 A245612(n) = if(n<2,1+n,if(!(n%2),(3*A245612(n/2))-1,A254049(A245612((n-1)/2))));
%o A305432 A289814(n) = { my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==2, 1, 0)), 2); } \\ From A289814
%o A305432 A291763(n) = A289814(A245612(n));
%o A305432 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
%o A305432 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A305432 A278222(n) = A046523(A005940(1+n));
%o A305432 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 A305432 v305432 = rgs_transform(vector(65538,n,A278222(A291763(n-1))));
%o A305432 A305432(n) = v305432[1+n];
%Y A305432 Cf. A245612, A278222, A291763, A305298, A305431, A305433.
%Y A305432 Cf. also A305302.
%K A305432 nonn
%O A305432 0,2
%A A305432 _Antti Karttunen_, Jun 01 2018