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

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, 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, 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

Offset: 0

Author

Antti Karttunen, Nov 16 2016

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16384

Crossrefs

Cf. A046523, A075157, A075159, A286617 (rgs-version of this filter).

Other base-2 related filter sequences: A278219, A278222.

Sequences that partition N into same or coarser equivalence classes are at least these: A092339, A227185.

Programs

PARI

A005811(n) = hammingweight(bitxor(n, n>>1));  \\ This function from Gheorghe Coserea, Sep 03 2015
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 };
A075157(n) = if(!n,n,(prime(A005811(n))*A286468(n))-1);
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
A278217(n) = A046523(1+A075157(n)); \\ From Antti Karttunen, May 17 2017

Scheme

(define (A278217 n) (A046523 (+ 1 (A075157 n))))
(define (A278217 n) (A046523 (A075159 (+ 1 n))))

Formula

a(n) = A046523(1+A075157(n)) = A046523(A075159(1+n)).