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A286621
Restricted growth sequence computed for filter-sequence A278221, related to the conjugated prime factorization (see A122111).
29
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, 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, 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
OFFSET
1,2
COMMENTS
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).
For example, for all i, j: a(i) = a(j) => A006530(i) = A006530(j).
LINKS
FORMULA
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).
EXAMPLE
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.
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.
For n=4, A278221(4) = 2, which was already encountered as A278221(2), thus we set a(4) = a(2) = 2.
For n=9, A278221(9) = 4, which was already encountered at n=3, thus a(9) = 3.
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.
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.
For n=388, A278221(388) = 50331648, which was already encountered at n=194, thus a(388) = a(194) = 106.
PROG
(PARI)
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; };
write_to_bfile(start_offset, vec, bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
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)};
A122111(n) = if(1==n, n, prime(bigomega(n))*A122111(A064989(n)));
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
write_to_bfile(1, rgs_transform(vector(10000, n, A278221(n))), "b286621.txt");
CROSSREFS
Cf. also A101296, A286603, A286605, A286610, A286619, A286622, A286626, A286378 for similarly constructed sequences.
Sequence in context: A332900 A336150 A336151 * A295876 A336147 A322590
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 11 2017
STATUS
approved