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A304738 Restricted growth sequence transform of A278222(A048673(n)).

%I A304738 #7 May 18 2018 19:45:25
%S A304738 1,1,2,3,1,1,2,4,5,5,4,6,3,3,3,7,3,5,2,1,4,3,8,3,5,5,9,5,1,10,5,11,3,
%T A304738 6,6,6,7,5,10,12,5,10,2,13,5,5,14,15,11,7,2,10,8,11,6,16,6,11,17,11,3,
%U A304738 4,7,18,8,5,3,10,7,6,7,16,3,17,19,5,3,1,7,6,20,3,10,17,5,6,6,5,5,6,11,5,20,3,7,5,14,15,10,21,5,11,14,13,5
%N A304738 Restricted growth sequence transform of A278222(A048673(n)).
%C A304738 Sequence allots a distinct value for each distinct multiset formed from the lengths of 1-runs in the binary representation of A048673(n). Compare to the scatter plot of A286622.
%H A304738 Antti Karttunen, <a href="/A304738/b304738.txt">Table of n, a(n) for n = 1..65539</a>
%H A304738 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A304738 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%o A304738 (PARI)
%o A304738 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 A304738 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
%o A304738 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A304738 A278222(n) = A046523(A005940(1+n));
%o A304738 A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
%o A304738 A048673(n) = (A003961(n)+1)/2;
%o A304738 v304738 = rgs_transform(vector(65539,n,A278222(A048673(n))));
%o A304738 A304738(n) = v304738[n];
%Y A304738 Cf. A003961, A048673, A278222, A286622.
%Y A304738 Cf. also A286243, A304101, A304737.
%K A304738 nonn
%O A304738 1,3
%A A304738 _Antti Karttunen_, May 18 2018