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A300247 Restricted growth sequence transform of A286457(n), filter combining A078898(n) and A246277(n).

%I A300247 #10 Mar 03 2018 20:10:18
%S A300247 1,2,2,3,2,4,2,5,3,6,2,7,2,8,4,9,2,10,2,11,12,13,2,14,3,15,16,17,2,18,
%T A300247 2,19,20,21,4,22,2,23,24,25,2,26,2,27,28,29,2,30,3,31,32,33,2,34,12,
%U A300247 35,36,37,2,38,2,39,40,41,42,43,2,44,45,46,2,47,2,48,49,50,4,51,2,52,53,54,2,55,56,57,58,59,2,60,12,61,62,63,64,65,2,66
%N A300247 Restricted growth sequence transform of A286457(n), filter combining A078898(n) and A246277(n).
%C A300247 For all i, j:
%C A300247   a(i) = a(j) => A280492(i) = A280492(j).
%C A300247   a(i) = a(j) => A300248(i) = A300248(j).
%C A300247 The latter follows because A046523(n) = A046523(2*A246277(n)).
%H A300247 Antti Karttunen, <a href="/A300247/b300247.txt">Table of n, a(n) for n = 1..65537</a>
%H A300247 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%e A300247 a(65) = a(119) (= 42) because A078898(65) = A078898(119) = 5 (both numbers occur in column 5 of A083221) and because A246277(65) = A246277(119) = 7 (both numbers occur in column 7 of A246278). Note that 65 = 5*13 = prime(3)*prime(6) and 119 = 7*17 = prime(4)*prime(7) = A003961(65). A246277(n) contains complete information about the (relative) differences between prime indices in the prime factorization of n.
%o A300247 (PARI)
%o A300247 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 A300247 write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
%o A300247 A020639(n) = { if(1==n,n,vecmin(factor(n)[, 1])); };
%o A300247 A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A300247 A078898(n) = { if(n<=1,n, my(spf=A020639(n),k=1,m=n/spf); while(m>1,if(A020639(m)>=spf,k++); m--); (k)); }; \\ _Antti Karttunen_, Mar 03 2018
%o A300247 A246277(n) = { if(1==n, 0, while((n%2), n = A064989(n)); (n/2)); };
%o A300247 A286457(n) = if(1==n,0,(1/2)*(2 + ((A078898(n)+A246277(n))^2) - A078898(n) - 3*A246277(n)));
%o A300247 write_to_bfile(1,rgs_transform(vector(65537,n,A286457(n))),"b300247.txt");
%Y A300247 Cf. A078898, A246277, A286457.
%Y A300247 Cf. also A300248, A280492.
%K A300247 nonn,look
%O A300247 1,2
%A A300247 _Antti Karttunen_, Mar 03 2018