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A352888 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278219(A109812(i)) = A278219(A109812(j)), for all i, j >= 1.

%I A352888 #9 Apr 07 2022 12:15:37
%S A352888 1,2,2,1,2,3,4,2,5,6,7,5,6,5,2,1,5,6,4,3,7,6,4,8,7,6,5,1,2,9,10,7,11,
%T A352888 12,6,9,13,7,3,5,6,7,6,5,6,9,4,6,9,2,6,12,6,5,11,7,13,14,7,15,13,12,
%U A352888 16,9,14,11,12,5,6,7,11,12,6,5,5,1,4,13,7,8,15,16,12,11,9,10,12,11,12,10,14,17,14,16,18
%N A352888 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278219(A109812(i)) = A278219(A109812(j)), for all i, j >= 1.
%C A352888 Restricted growth sequence transform of A278219(A109812(n)).
%C A352888 For all i, j: a(i) = a(j) => A352889(i) = A352889(j).
%H A352888 Antti Karttunen, <a href="/A352888/b352888.txt">Table of n, a(n) for n = 1..100000</a>
%H A352888 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%o A352888 (PARI)
%o A352888 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 A352888 v109812 = readvec("b109812_to10e5.txt"); \\ Prepared from b-file data with gawk ' { print $2 } '
%o A352888 up_to = #v109812;
%o A352888 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
%o A352888 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A352888 A003188(n) = bitxor(n, n>>1);
%o A352888 A278219(n) = A046523(A005940(1+A003188(n)));
%o A352888 A109812(n) = v109812[n];
%o A352888 v352888 = rgs_transform(vector(up_to, n, A278219(A109812(n))));
%o A352888 A352888(n) = v352888[n];
%Y A352888 Cf. A109812, A278219, A352889.
%Y A352888 Cf. also A286619, A351578, A351963.
%K A352888 nonn,base,look
%O A352888 1,2
%A A352888 _Antti Karttunen_, Apr 07 2022