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A304737 Restricted growth sequence transform of A278222(A064413(n)).

%I A304737 #8 May 18 2018 19:45:17
%S A304737 1,1,1,2,2,3,2,1,3,3,4,3,5,5,6,2,1,3,7,7,3,8,4,7,7,5,7,7,9,3,1,3,3,8,
%T A304737 6,7,7,9,10,3,7,9,9,6,2,7,7,8,5,7,11,4,12,3,7,9,9,13,3,14,14,13,3,1,3,
%U A304737 6,6,15,10,9,7,3,6,6,15,6,6,10,7,10,10,3,10,16,17,7,9,18,18,10,2,7,19,7,8,8,10,8,10,10,17,9,12,5,9
%N A304737 Restricted growth sequence transform of A278222(A064413(n)).
%C A304737 Sequence allots a distinct value for each distinct multiset formed from the lengths of 1-runs in the binary representation of A064413(n), the n-th term of EKG-sequence. Compare to the scatter plot of A286622.
%H A304737 Antti Karttunen, <a href="/A304737/b304737.txt">Table of n, a(n) for n = 1..65539</a>
%H A304737 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A304737 <a href="/index/Ed#EKG">Index entries for sequences related to EKG sequence</a>
%o A304737 (PARI)
%o A304737 \\ Needs also code for A064413.
%o A304737 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 A304737 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
%o A304737 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A304737 A278222(n) = A046523(A005940(1+n));
%o A304737 v304737 = rgs_transform(vector(65539,n,A278222(A064413(n))));
%o A304737 A304737(n) = v304737[n];
%Y A304737 Cf. A064301, A064413, A278222, A286622.
%Y A304737 Cf. also A304738.
%K A304737 nonn
%O A304737 1,4
%A A304737 _Antti Karttunen_, May 18 2018