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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 October 23 09:28 EDT 2019. Contains 328345 sequences. (Running on oeis4.)