cp's OEIS Frontend

A305303 Restricted growth sequence transform of ordered pair [A278222(A304760(n)), A278222(A291760(n))], constructed from runlengths of 1-digits and 2-digits in base-3 representation of A254103(n).

%I A305303 #10 Jul 21 2025 00:02:04
%S A305303 1,2,3,2,4,5,6,3,7,2,4,4,8,9,10,11,12,7,13,4,14,3,15,5,16,5,7,4,17,2,
%T A305303 4,14,18,4,8,14,19,20,21,6,22,22,23,11,8,24,10,4,25,22,23,4,22,7,26,4,
%U A305303 27,21,28,7,14,4,8,10,29,16,30,14,17,4,8,31,32,9,12,8,27,12,19,24,33,14,17,10,34,2,4,22,16,11,14,14,17,3,15,11,35,14,17,31,34
%N A305303 Restricted growth sequence transform of ordered pair [A278222(A304760(n)), A278222(A291760(n))], constructed from runlengths of 1-digits and 2-digits in base-3 representation of A254103(n).
%C A305303 Restricted growth sequence transform of A290093(A254103(n)).
%C A305303 For all i, j: a(i) = a(j) => A286633(i) = A286633(j) => A286632(i) = A286632(j).
%H A305303 Antti Karttunen, <a href="/A305303/b305303.txt">Table of n, a(n) for n = 0..65537</a>
%o A305303 (PARI)
%o A305303 A254103(n) = if(!n,n,if(!(n%2),(3*A254103(n/2))-1,(3*(1+A254103((n-1)/2)))\2));
%o A305303 A289813(n) = { my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==1, 1, 0)), 2); } \\ From A289813
%o A305303 A289814(n) = { my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==2, 1, 0)), 2); } \\ From A289813
%o A305303 A304760(n) = A289813(A254103(n));
%o A305303 A291760(n) = A289814(A254103(n));
%o A305303 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
%o A305303 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A305303 A278222(n) = A046523(A005940(1+n));
%o A305303 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 A305303 Aux305303(n) = [A278222(A304760(n)), A278222(A291760(n))];
%o A305303 v305303 = rgs_transform(vector(65538,n,Aux305303(n-1)));
%o A305303 A305303(n) = v305303[1+n];
%Y A305303 Cf. A254103, A289813, A289814, A291760, A304740, A304746, A304760.
%Y A305303 Cf. also A286632, A286633, A290093, A290094, A305301, A305302.
%K A305303 nonn,base
%O A305303 0,2
%A A305303 _Antti Karttunen_, May 30 2018