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A278217 Filter-sequence related to base-2 run-length encoding: a(n) = A046523(A075159(1+n)) = A046523(1+A075157(n)).

%I A278217 #24 Dec 01 2021 03:53:05
%S A278217 1,2,2,4,6,2,4,8,12,6,2,6,12,4,8,16,24,12,6,30,6,2,6,12,36,12,4,12,24,
%T A278217 8,16,32,48,24,12,60,30,6,30,60,12,6,2,6,30,6,12,24,72,36,12,60,12,4,
%U A278217 12,36,72,24,8,24,48,16,32,64,96,48,24,120,60,12,60,180,60,30,6,30,210,30,60,120,24,12,6,30,6,2,6,12,60,30,6,30,60,12,24,48,144,72
%N A278217 Filter-sequence related to base-2 run-length encoding: a(n) = A046523(A075159(1+n)) = A046523(1+A075157(n)).
%H A278217 Antti Karttunen, <a href="/A278217/b278217.txt">Table of n, a(n) for n = 0..16384</a>
%F A278217 a(n) = A046523(1+A075157(n)) = A046523(A075159(1+n)).
%o A278217 (PARI)
%o A278217 A005811(n) = hammingweight(bitxor(n, n>>1));  \\ This function from _Gheorghe Coserea_, Sep 03 2015
%o A278217 A286468(n) = { my(p=((n+1)%2), i=0, m=1); while(n>0, if(((n%2)==p), m *= prime(i), p = (n%2); i = i+1); n = n\2); m };
%o A278217 A075157(n) = if(!n,n,(prime(A005811(n))*A286468(n))-1);
%o A278217 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
%o A278217 A278217(n) = A046523(1+A075157(n)); \\ From _Antti Karttunen_, May 17 2017
%o A278217 (Scheme)
%o A278217 (define (A278217 n) (A046523 (+ 1 (A075157 n))))
%o A278217 (define (A278217 n) (A046523 (A075159 (+ 1 n))))
%Y A278217 Cf. A046523, A075157, A075159, A286617 (rgs-version of this filter).
%Y A278217 Other base-2 related filter sequences: A278219, A278222.
%Y A278217 Sequences that partition N into same or coarser equivalence classes are at least these: A092339, A227185.
%K A278217 nonn
%O A278217 0,2
%A A278217 _Antti Karttunen_, Nov 16 2016