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A351963 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(A109812(i)) = A278222(A109812(j)), for all i, j >= 1.

%I A351963 #18 Apr 07 2022 09:27:23
%S A351963 1,1,1,2,1,3,3,1,2,3,3,2,3,4,1,4,2,3,3,5,3,5,3,6,3,5,2,7,1,5,6,3,5,5,
%T A351963 3,5,6,3,8,2,9,3,5,4,5,5,3,8,5,1,8,5,3,7,5,3,10,6,3,6,6,5,6,5,6,5,5,4,
%U A351963 8,3,9,5,5,7,2,11,3,10,3,10,6,6,9,5,8,6,5,8,5,10,6,12,6,10,6,5,10,4,6,8,5,13
%N A351963 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(A109812(i)) = A278222(A109812(j)), for all i, j >= 1.
%C A351963 Restricted growth sequence transform of A278222(A109812(n)), or equally of, A278222(A351965(n)).
%C A351963 For all i, j: A351578(i) = A351578(j) => a(i) = a(j) => A352884(i) = A352884(j).
%H A351963 Antti Karttunen, <a href="/A351963/b351963.txt">Table of n, a(n) for n = 1..100000</a>
%H A351963 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%o A351963 (PARI)
%o A351963 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 A351963 v109812 = readvec("b109812_to10e5.txt"); \\ Prepared from b-file data with gawk ' { print $2 } '
%o A351963 up_to = #v109812;
%o A351963 A109812(n) = v109812[n];
%o A351963 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
%o A351963 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
%o A351963 v351963 = rgs_transform(vector(up_to, n, A046523(A005940(1+A109812(n)))));
%o A351963 A351963(n) = v351963[n];
%Y A351963 Cf. A005940, A046523, A109812, A278222, A286622, A351965, A352884.
%Y A351963 Cf. also A351578, A352888.
%K A351963 nonn,base
%O A351963 1,4
%A A351963 _Antti Karttunen_, Apr 06 2022