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A352899 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = A352892(n), except f(n) = -n when <= 2.

%I A352899 #14 Apr 09 2022 13:25:56
%S A352899 1,2,3,4,3,3,3,5,6,7,3,8,3,9,4,10,3,4,3,11,12,13,3,14,6,15,7,16,3,3,3,
%T A352899 17,8,18,4,19,3,20,21,22,3,7,3,23,5,24,3,25,6,26,27,28,3,5,12,29,30,
%U A352899 31,3,27,3,32,26,33,8,9,3,34,35,36,3,37,3,38,9,39,4,13,3,40,41,42,3,43,21,44,45,46,3,8,12
%N A352899 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = A352892(n), except f(n) = -n when <= 2.
%C A352899 Restricted growth sequence transform of function f(n) = -n if n < 3, and otherwise f(n) = A352892(n).
%C A352899 For all i, j:
%C A352899   A305801(i) = A305801(j) => A352898(i) = A352898(j) => a(i) = a(j),
%C A352899   a(i) = a(j) => A352893(i) = A352893(j),
%C A352899   a(i) = a(j) => A352896(i) = A352896(j).
%H A352899 Antti Karttunen, <a href="/A352899/b352899.txt">Table of n, a(n) for n = 1..65537</a>
%H A352899 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%H A352899 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%o A352899 (PARI)
%o A352899 up_to = 65537;
%o A352899 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 A352899 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
%o A352899 A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A352899 A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
%o A352899 A329603(n) = A005940(2+(3*A156552(n)));
%o A352899 A341515(n) = if(n%2, A064989(n), A329603(n));
%o A352899 A348717(n) = { my(f=factor(n)); if(#f~>0, my(pi1=primepi(f[1, 1])); for(k=1, #f~, f[k, 1] = prime(primepi(f[k, 1])-pi1+1))); factorback(f); }; \\ From A348717
%o A352899 A352892(n) = A348717(A341515(n));
%o A352899 Aux352899(n) = if(n<=2,-n,A352892(n));
%o A352899 v352899 = rgs_transform(vector(up_to, n, Aux352899(n)));
%o A352899 A352899(n) = v352899[n];
%Y A352899 Cf. A305801, A329603, A341515, A348717, A352892, A352893, A352896, A352898.
%K A352899 nonn
%O A352899 1,2
%A A352899 _Antti Karttunen_, Apr 08 2022