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A305431 Restricted growth sequence transform of A278222(A305295(n)), constructed from runlengths of 1-digits in base-3 representation of A245612(n).

%I A305431 #9 Jul 20 2025 17:58:48
%S A305431 1,2,1,1,3,4,2,3,4,1,3,1,1,2,1,2,5,6,2,7,8,4,2,1,3,7,1,4,7,7,1,1,9,1,
%T A305431 7,10,1,11,1,2,12,8,5,7,1,1,2,8,4,7,1,7,7,8,3,2,8,7,1,7,7,1,2,1,13,14,
%U A305431 7,11,6,1,12,14,3,11,8,8,7,15,1,16,10,17,3,17,16,3,1,15,3,1,7,7,1,1,7,6,5,7,6,1,7,11,1,8,8,1
%N A305431 Restricted growth sequence transform of A278222(A305295(n)), constructed from runlengths of 1-digits in base-3 representation of A245612(n).
%H A305431 Antti Karttunen, <a href="/A305431/b305431.txt">Table of n, a(n) for n = 0..65537</a>
%o A305431 (PARI)
%o A305431 A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
%o A305431 A048673(n) = (A003961(n)+1)/2;
%o A305431 A254049(n) = A048673((2*n)-1);
%o A305431 A245612(n) = if(n<2,1+n,if(!(n%2),(3*A245612(n/2))-1,A254049(A245612((n-1)/2))));
%o A305431 A289813(n) = { my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==1, 1, 0)), 2); } \\ From A289813
%o A305431 A305295(n) = A289813(A245612(n));
%o A305431 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
%o A305431 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A305431 A278222(n) = A046523(A005940(1+n));
%o A305431 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 A305431 v305431 = rgs_transform(vector(65538,n,A278222(A305295(n-1))));
%o A305431 A305431(n) = v305431[1+n];
%Y A305431 Cf. A245612, A278222, A305295, A305296, A305432, A305433.
%Y A305431 Cf. also A305301.
%K A305431 nonn
%O A305431 0,2
%A A305431 _Antti Karttunen_, Jun 01 2018