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A332901 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(A332896(i)) = A278222(A332896(j)) for all i, j.

%I A332901 #11 Mar 04 2020 18:09:25
%S A332901 1,1,2,1,2,2,3,1,1,2,4,2,3,3,3,1,4,1,5,2,2,4,6,2,1,3,2,3,5,3,7,1,3,4,
%T A332901 8,1,6,5,4,2,7,2,9,4,2,6,10,2,1,1,5,3,9,2,11,3,4,5,12,3,10,7,3,1,2,3,
%U A332901 13,4,5,8,14,1,12,6,2,5,2,4,15,2,1,7,16,2,3,9,6,4,13,2,17,6,6,10,18,2,14,1,4,1,15,5,19,3,3
%N A332901 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(A332896(i)) = A278222(A332896(j)) for all i, j.
%C A332901 Restricted growth sequence transform of A278222(A332896(n)).
%C A332901 This is a variant of A292583: Instead of runs of numbers of the form 4k+3 encountered on trajectories of the standard Doudna-tree (A005940), this relates to the corresponding trajectories in A332815-tree. See comments in A292583.
%C A332901 For all i, j:
%C A332901   a(i) = a(j) => A053866(i) = A053866(j),
%C A332901   a(i) = a(j) => A332898(i) = A332898(j).
%H A332901 Antti Karttunen, <a href="/A332901/b332901.txt">Table of n, a(n) for n = 1..65537</a>
%o A332901 (PARI)
%o A332901 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940
%o A332901 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A332901 A278222(n) = A046523(A005940(1+n));
%o A332901 v332901 = rgs_transform(vector(up_to,n,A278222(A332896(n))));
%o A332901 A332901(n) = v332901[n];
%Y A332901 Cf. A053866, A278222, A332896, A332898, A332900.
%Y A332901 Cf. A028982 (positions of ones).
%Y A332901 Cf. also A292583.
%K A332901 nonn
%O A332901 1,3
%A A332901 _Antti Karttunen_, Mar 04 2020