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 A286622 Restricted growth sequence computed for filter-sequence A278222, related to 1-runs in the binary representation of n. 40
 1, 2, 2, 3, 2, 4, 3, 5, 2, 4, 4, 6, 3, 6, 5, 7, 2, 4, 4, 6, 4, 8, 6, 9, 3, 6, 6, 10, 5, 9, 7, 11, 2, 4, 4, 6, 4, 8, 6, 9, 4, 8, 8, 12, 6, 12, 9, 13, 3, 6, 6, 10, 6, 12, 10, 14, 5, 9, 9, 14, 7, 13, 11, 15, 2, 4, 4, 6, 4, 8, 6, 9, 4, 8, 8, 12, 6, 12, 9, 13, 4, 8, 8, 12, 8, 16, 12, 17, 6, 12, 12, 18, 9, 17, 13, 19, 3, 6, 6, 10, 6, 12, 10, 14, 6, 12, 12, 18, 10, 18 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS When filtering sequences (by equivalence class partitioning), this sequence can be used instead of A278222, because for all i, j it holds that: a(i) = a(j) <=> A278222(i) = A278222(j). For example, for all i, j: a(i) = a(j) => A000120(i) = A000120(j), and for all i, j: a(i) = a(j) => A001316(i) = A001316(j). The sequence allots a distinct value for each distinct multiset formed from the lengths of 1-runs in the binary representation of n. See the examples. - Antti Karttunen, Jun 04 2017 LINKS Antti Karttunen, Table of n, a(n) for n = 0..65537 EXAMPLE For n = 0, there are no 1-runs, thus the multiset is empty [], and it is allotted the number 1, thus a(0) = 1. For n = 1, in binary also "1", there is one 1-run of length 1, thus the multiset is , which has not been encountered before, and a new number is allotted for that, thus a(1) = 2. For n = 2, in binary "10", there is one 1-run of length 1, thus the multiset is , which was already encountered at n=1, thus a(2) = a(1) = 2. For n = 3, in binary "11", there is one 1-run of length 2, thus the multiset is , which has not been encountered before, and a new number is allotted for that, thus a(3) = 3. For n = 4, in binary "100", there is one 1-run of length 1, thus the multiset is , which was already encountered at n=1 for the first time, thus a(4) = a(1) = 2. For n = 5, in binary "101", there are two 1-runs, both of length 1, thus the multiset is [1,1], which has not been encountered before, and a new number is allotted for that, thus a(5) = 4. 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])); } A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ Modified from code of M. F. Hasler 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 A278222(n) = A046523(A005940(1+n)); v286622 = rgs_transform(vector(1+65537, n, A278222(n-1))); A286622(n) = v286622[1+n]; CROSSREFS Cf. A278222, A000120, A001316. Cf. A286552 (ordinal transform). Cf. also A101296, A286581, A286589, A286597, A286599, A286600, A286602, A286603, A286605, A286610, A286619, A286621, A286626, A286378, A304101 for similarly constructed or related sequences. Cf. also A305793, A305795. Sequence in context: A232479 A162897 A286532 * A286589 A246029 A245564 Adjacent sequences:  A286619 A286620 A286621 * A286623 A286624 A286625 KEYWORD nonn,look AUTHOR Antti Karttunen, May 11 2017 EXTENSIONS Example section added by Antti Karttunen, Jun 04 2017 STATUS approved

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Last modified January 21 04:53 EST 2020. Contains 331104 sequences. (Running on oeis4.)