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A302795 Restricted growth sequence transform of A278222(A302793(n)).

%I A302795 #11 Apr 27 2018 04:14:02
%S A302795 1,2,3,4,2,3,2,5,6,4,2,7,4,7,4,3,5,4,2,7,4,8,9,6,7,7,10,3,7,10,5,11,9,
%T A302795 9,2,7,4,8,12,4,7,8,12,13,8,9,7,14,4,7,10,3,7,6,7,15,12,9,5,15,4,14,
%U A302795 16,9,11,4,2,7,12,8,9,4,7,8,9,4,8,10,7,14,12,8,12,12,8,12,8,17,4,18,7,19,12,17,4,9,14,7,12,3,7,10,7,15,12,12
%N A302795 Restricted growth sequence transform of A278222(A302793(n)).
%H A302795 Antti Karttunen, <a href="/A302795/b302795.txt">Table of n, a(n) for n = 0..65537</a>
%H A302795 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%o A302795 (PARI)
%o A302795 rgs_transform(invec) = { my(occurrences = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(occurrences,invec[i]), my(pp = mapget(occurrences, invec[i])); outvec[i] = outvec[pp] , mapput(occurrences,invec[i],i); outvec[i] = u; u++ )); outvec; };
%o A302795 write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
%o A302795 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ After code in A005940
%o A302795 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A302795 A278222(n) = A046523(A005940(1+n));
%o A302795 A193231(n) = { my(x='x); subst(lift(Mod(1, 2)*subst(Pol(binary(n), x), x, 1+x)), x, 2) }; \\ From A193231
%o A302795 A302793(n) = if(!n,n,A193231(1+A193231(n-1)));
%o A302795 write_to_bfile(0,rgs_transform(vector(65538,n,A278222(A302793(n-1)))),"b302795.txt");
%Y A302795 Cf. A278222, A302793.
%Y A302795 Cf. also A286602, A286622 (compare the scatter-plots).
%K A302795 nonn,base,look
%O A302795 0,2
%A A302795 _Antti Karttunen_, Apr 26 2018