A286619 - OEIS

A286619

Restricted growth sequence computed for filter-sequence A278219, related to run-lengths in the binary representation of n.

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

(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 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).

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..65537

Index entries for sequences related to binary expansion of n

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);

A278219(n) = A278222(A003188(n));

write_to_bfile(0, rgs_transform(vector(65538, n, A278219(n-1))), "b286619.txt");

CROSSREFS

Cf. A278219, A005811, A073334.

Cf. also A101296, A286603, A286605, A286610, A286621, A286622, A286626, A286378 for similarly constructed sequences.

Sequence in context: A339902 A286581 A286599 * A286534 A324532 A324390

Adjacent sequences: A286616 A286617 A286618 * A286620 A286621 A286622

KEYWORD

nonn,look

AUTHOR

Antti Karttunen, May 11 2017

STATUS

approved