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A323892 Lexicographically earliest sequence such that a(i) = a(j) => A002487(i) = A002487(j) and A033879(i) = A033879(j), for all i, j >= 1.

%I A323892 #7 Feb 10 2019 23:05:55
%S A323892 1,1,2,1,3,4,5,1,6,7,8,9,10,3,11,1,12,13,14,15,16,17,18,19,20,8,21,22,
%T A323892 23,24,25,1,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,
%U A323892 45,46,35,47,48,49,50,51,52,53,54,55,1,56,57,58,8,59,60,61,62,63,64,65,66,67,68,69,70,71,47,72,73,74,75,76,77,78,79,80,31,81
%N A323892 Lexicographically earliest sequence such that a(i) = a(j) => A002487(i) = A002487(j) and A033879(i) = A033879(j), for all i, j >= 1.
%C A323892 Restricted growth sequence transform of the ordered pair [A002487(n), A033879(n)].
%H A323892 Antti Karttunen, <a href="/A323892/b323892.txt">Table of n, a(n) for n = 1..65537</a>
%H A323892 <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>
%F A323892 a(2^n) = 1 for all n >= 0.
%o A323892 (PARI)
%o A323892 up_to = 65537;
%o A323892 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 A323892 A002487(n) = { my(a=1, b=0); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); (b); }; \\ From A002487
%o A323892 A033879(n) = (2*n-sigma(n));
%o A323892 A323892aux(n) = [A002487(n), A033879(n)];
%o A323892 v323892 = rgs_transform(vector(up_to,n,A323892aux(n)));
%o A323892 A323892(n) = v323892[n];
%Y A323892 Cf. A002487, A033879.
%Y A323892 Cf. also A318310, A323889.
%K A323892 nonn
%O A323892 1,3
%A A323892 _Antti Karttunen_, Feb 09 2019