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A286619
Restricted growth sequence computed for filter-sequence A278219, related to run-lengths in the binary representation of n.
20
1, 2, 3, 2, 3, 4, 5, 2, 3, 6, 7, 4, 5, 6, 5, 2, 3, 6, 8, 6, 7, 9, 10, 4, 5, 11, 10, 6, 5, 6, 5, 2, 3, 6, 8, 6, 8, 12, 13, 6, 7, 14, 15, 9, 10, 12, 10, 4, 5, 11, 13, 11, 10, 14, 13, 6, 5, 11, 10, 6, 5, 6, 5, 2, 3, 6, 8, 6, 8, 12, 13, 6, 8, 16, 17, 12, 13, 16, 13, 6, 7, 14, 17, 14, 15, 18, 19, 9, 10, 20, 21, 12, 10, 12, 10, 4, 5, 11, 13, 11, 13, 20, 22, 11, 10
OFFSET
0,2
COMMENTS
When filtering sequences (by equivalence class partitioning), this sequence can be used instead of A278219, because for all i, j it holds that: a(i) = a(j) <=> A278219(i) = A278219(j).
For example, for all i, j: a(i) = a(j) => A005811(i) = A005811(j). (The same is true for A073334, as it is a sequence computed from A005811).
MATHEMATICA
f[n_, i_, x_] := Which[n == 0, x, EvenQ@ n, f[n/2, i + 1, x], True, f[(n - 1)/2, i, x Prime@ i]]; g[n_] := If[n == 1, 1, Times @@ MapIndexed[Prime[First@ #2]^#1 &, Sort[FactorInteger[n][[All, -1]], Greater]]]; With[{nn = 99}, Function[s, Table[Position[Keys@ s, k_ /; MemberQ[k, n]][[1, 1]], {n, nn}]]@ Map[#1 -> #2 & @@ # &, Transpose@ {Values@ #, Keys@ #}] &@ PositionIndex@ Table[g@ f[BitXor[n, Floor[n/2]], 1, 1], {n, 0, nn}]] (* Michael De Vlieger, May 12 2017, Version 10 *)
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));
A003188(n) = bitxor(n, n>>1);
write_to_bfile(0, rgs_transform(vector(65538, n, A278219(n-1))), "b286619.txt");
CROSSREFS
Cf. also A101296, A286603, A286605, A286610, A286621, A286622, A286626, A286378 for similarly constructed sequences.
Sequence in context: A339902 A286581 A286599 * A286534 A324532 A324390
KEYWORD
nonn,look
AUTHOR
Antti Karttunen, May 11 2017
STATUS
approved