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%I #10 Jun 10 2020 05:24:42
%S 1,1,1,2,1,3,2,3,1,4,3,5,2,6,3,7,1,8,4,9,3,10,5,5,2,10,6,5,3,8,7,5,1,
%T 11,8,12,4,13,9,14,3,15,10,16,5,10,5,17,2,15,10,16,6,10,5,10,3,18,8,
%U 19,7,3,5,5,1,20,11,20,8,21,12,22,4,22,13,23,9,8,14,20,3,22,15,22,10,24,16,25,5,26,10,14,5,20,17,27,2,22,15,23,10,10,16,28,6,26
%N Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(A335422(i)) = A046523(A335422(j)) for all i, j >= 0.
%C For all i, j: A324400(i) = A324400(j) => a(i) = a(j) => A335420(i) = A335420(j).
%H Antti Karttunen, <a href="/A335421/b335421.txt">Table of n, a(n) for n = 0..65537</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F For all n >= 0, a(2^n) = 1.
%o (PARI)
%o up_to = 65537;
%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 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 A054429(n) = ((3<<#binary(n\2))-n-1); \\ From A054429
%o A163511(n) = if(!n,1,A005940(1+A054429(n)))
%o A335422(n) = A005940(1+A163511(n));
%o v335421 = rgs_transform(vector(1+up_to,n,A046523(A335422(n-1))));
%o A335421(n) = v335421[1+n];
%Y Cf. A046523, A335420, A335422.
%Y Cf. also A286622, A324400.
%K nonn,look
%O 0,4
%A _Antti Karttunen_, Jun 09 2020
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