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A336154 Lexicographically earliest infinite sequence such that a(i) = a(j) => A007814(1+i) = A007814(1+j) and A278222(i) = A278222(j), for all i, j >= 1.

%I A336154 #7 Jul 11 2020 17:58:05
%S A336154 1,2,3,2,4,5,6,2,4,7,8,5,9,10,11,2,4,7,8,7,12,13,14,5,9,13,15,10,16,
%T A336154 17,18,2,4,7,8,7,12,13,14,7,12,19,20,13,21,22,23,5,9,13,15,13,21,24,
%U A336154 25,10,16,22,26,17,27,28,29,2,4,7,8,7,12,13,14,7,12,19,20,13,21,22,23,7,12,19,20,19,30,31,32,13,21,31,33,22,34,35,36,5,9,13,15,13,21,24,25,13,21
%N A336154 Lexicographically earliest infinite sequence such that a(i) = a(j) => A007814(1+i) = A007814(1+j) and A278222(i) = A278222(j), for all i, j >= 1.
%C A336154 Restricted growth sequence transform of the ordered pair [A007814(1+n), A278222(n)]. Note that A007814(1+n) gives the number of trailing 1-bits in the binary expansion of n.
%C A336154 For all i, j: A324400(i) = A324400(j) => a(i) = a(j).
%H A336154 Antti Karttunen, <a href="/A336154/b336154.txt">Table of n, a(n) for n = 1..65537</a>
%H A336154 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%o A336154 (PARI)
%o A336154 up_to = 65537;
%o A336154 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 A336154 A007814(n) = valuation(n,2);
%o A336154 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
%o A336154 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A336154 A278222(n) = A046523(A005940(1+n));
%o A336154 Aux336154(n) = [A007814(1+n), A278222(n)];
%o A336154 v336154 = rgs_transform(vector(up_to, n, Aux336154(n)));
%o A336154 A336154(n) = v336154[n];
%Y A336154 Cf. A007814, A278222.
%Y A336154 Cf. also A286622, A324400, A336153, A336155, A336156.
%K A336154 nonn
%O A336154 1,2
%A A336154 _Antti Karttunen_, Jul 11 2020