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 A286621 Restricted growth sequence computed for filter-sequence A278221, related to the conjugated prime factorization (see A122111). 16

%I

%S 1,2,3,2,4,5,6,2,3,7,8,5,9,10,7,2,11,5,12,7,13,14,15,5,4,16,3,10,17,

%T 18,19,2,20,21,10,5,22,23,24,7,25,26,27,14,7,28,29,5,6,7,30,16,31,5,

%U 20,10,32,33,34,18,35,36,13,2,37,38,39,21,40,26,41,5,42,43,7,23,14,44,45,7,3,46,47,26,48,49,50,14,51,18,24,28,52,53,54,5,55,10,20,7

%N Restricted growth sequence computed for filter-sequence A278221, related to the conjugated prime factorization (see A122111).

%C When filtering sequences (by equivalence class partitioning), this sequence (with its modestly sized terms) can be used instead of A278221 (which has some huge terms), because for all i, j it holds that: a(i) = a(j) <=> A278221(i) = A278221(j).

%C For example, for all i, j: a(i) = a(j) => A006530(i) = A006530(j).

%H Antti Karttunen, <a href="/A286621/b286621.txt">Table of n, a(n) for n = 1..10000</a>

%F Construction: we start with a(1)=1 for A278221(1)=1, and then after, for all n > 1, we use the least so far unused natural number k for a(n) if A278221(n) has not been encountered before, otherwise [whenever A278221(n) = A278221(m), for some m < n], we set a(n) = a(m).

%e For n=2, A278221(2) = 2, which has not been encountered before, thus we allot for a(2) the least so far unused number, which is 2, thus a(2) = 2.

%e For n=3, A278221(3) = 4, which has not been encountered before, thus we allot for a(3) the least so far unused number, which is 3, thus a(3) = 3.

%e For n=4, A278221(4) = 2, which was already encountered as A278221(2), thus we set a(4) = a(2) = 2.

%e For n=9, A278221(9) = 4, which was already encountered at n=3, thus a(9) = 3.

%e For n=13, A278221(13) = 64, which has not been encountered before, thus we allot for a(13) the least so far unused number, which is 9, thus a(13) = 9.

%e For n=194, A278221(194) = 50331648, which has not been encountered before, thus we allot for a(194) the least so far unused number, which is 106, thus a(194) = 106.

%e For n=388, A278221(388) = 50331648, which was already encountered at n=194, thus a(388) = a(194) = 106.

%o (PARI)

%o rgs_transform(invec) = { my(occurrences = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(occurrences,invec[i]), my(pp = mapget(occurrences, invec[i])); outvec[i] = outvec[pp] , mapput(occurrences,invec[i],i); outvec[i] = u; u++ )); outvec; };

%o write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }

%o 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 A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));

%o A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ This function from _Charles R Greathouse IV_, Aug 17 2011

%o A278221(n) = A046523(A122111(n));

%o write_to_bfile(1,rgs_transform(vector(10000,n,A278221(n))),"b286621.txt");

%Y Cf. A278221, A006530, A122111.

%Y Cf. also A101296, A286603, A286605, A286610, A286619, A286622, A286626, A286378 for similarly constructed sequences.

%K nonn

%O 1,2

%A _Antti Karttunen_, May 11 2017

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Last modified January 17 23:37 EST 2020. Contains 330995 sequences. (Running on oeis4.)