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A323897 Lexicographically earliest sequence such that a(i) = a(j) => A002487(i) = A002487(j) and A083254(i) = A083254(j), for all i, j >= 1.

%I A323897 #6 Feb 10 2019 23:06:03
%S A323897 1,2,3,2,4,5,6,2,7,8,9,10,11,8,12,2,13,14,15,16,17,18,19,20,21,18,22,
%T A323897 16,23,24,25,2,26,18,27,28,29,30,31,32,33,34,35,36,37,30,38,39,40,41,
%U A323897 42,36,43,34,44,32,45,30,46,47,48,18,49,2,50,51,52,36,53,54,55,56,57,58,59,60,61,62,63,64,65,58,66,67,68,69,70,71,72,73,74,60,75
%N A323897 Lexicographically earliest sequence such that a(i) = a(j) => A002487(i) = A002487(j) and A083254(i) = A083254(j), for all i, j >= 1.
%C A323897 Restricted growth sequence transform of the ordered pair [A002487(n), A083254(n)].
%H A323897 Antti Karttunen, <a href="/A323897/b323897.txt">Table of n, a(n) for n = 1..65537</a>
%H A323897 <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>
%F A323897 a(2^n) = 2 for all n >= 1.
%o A323897 (PARI)
%o A323897 up_to = 65537;
%o A323897 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 A323897 A002487(n) = { my(a=1, b=0); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); (b); }; \\ From A002487
%o A323897 A083254(n) = (2*eulerphi(n)-n);
%o A323897 A323897aux(n) = [A002487(n), A083254(n)];
%o A323897 v323897 = rgs_transform(vector(up_to,n,A323897aux(n)));
%o A323897 A323897(n) = v323897[n];
%Y A323897 Cf. A000010, A002487, A083254.
%Y A323897 Cf. also A323892, A323898.
%K A323897 nonn
%O A323897 1,2
%A A323897 _Antti Karttunen_, Feb 09 2019