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 A278219 Filter-sequence related to base-2 run length encoding: a(n) = A046523(A243353(n)). 15
 1, 2, 4, 2, 4, 8, 6, 2, 4, 12, 16, 8, 6, 12, 6, 2, 4, 12, 36, 12, 16, 32, 24, 8, 6, 30, 24, 12, 6, 12, 6, 2, 4, 12, 36, 12, 36, 72, 60, 12, 16, 48, 64, 32, 24, 72, 24, 8, 6, 30, 60, 30, 24, 48, 60, 12, 6, 30, 24, 12, 6, 12, 6, 2, 4, 12, 36, 12, 36, 72, 60, 12, 36, 180, 144, 72, 60, 180, 60, 12, 16, 48, 144, 48, 64, 128, 96, 32, 24, 120, 216, 72, 24, 72 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Antti Karttunen, Table of n, a(n) for n = 0..65537 FORMULA a(n) = A046523(A243353(n)). a(n) = A278222(A003188(n)). a(n) = A278220(1+A075157(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]]]; Table[g@ f[BitXor[n, Floor[n/2]], 1, 1], {n, 0, 93}] (* Michael De Vlieger, May 09 2017 *) PROG (Scheme) (define (A278219 n) (A046523 (A243353 n))) (Python) from sympy import prime, factorint import math def A(n): return n - 2**int(math.floor(math.log(n, 2))) def b(n): return n + 1 if n<2 else prime(1 + (len(bin(n)[2:]) - bin(n)[2:].count("1"))) * b(A(n)) def a005940(n): return b(n - 1) def P(n):     f = factorint(n)     return sorted([f[i] for i in f]) def a046523(n):     x=1     while True:         if P(n) == P(x): return x         else: x+=1 def a003188(n): return n^int(n/2) def a243353(n): return a005940(1 + a003188(n)) def a(n): return a046523(a243353(n)) # Indranil Ghosh, May 07 2017 CROSSREFS Cf. A003188, A046523, A075157, A243353, A278220. Other base-2 related filter sequences: A278217, A278222. Sequences that (seem to) partition N into same or coarser equivalence classes are at least these: A005811, A136004, A033264, A037800, A069010, A087116, A090079 and many others like A105500, A106826, A166242, A246960, A277561, A037834, A225081 although these have not been fully checked yet. Sequence in context: A286580 A286598 A286557 * A155682 A191370 A298242 Adjacent sequences:  A278216 A278217 A278218 * A278220 A278221 A278222 KEYWORD nonn AUTHOR Antti Karttunen, Nov 16 2016 STATUS approved

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Last modified February 20 17:04 EST 2020. Contains 332080 sequences. (Running on oeis4.)