A278219 -id:A278219 - cp's OEIS frontend

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

Antti Karttunen, Nov 16 2016

nonn

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

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.

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

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

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

A366261 The least number with the same prime signature as A366260, where A366260 is Doudna sequence permuted by May code.

Original entry on oeis.org

1, 2, 4, 2, 4, 2, 6, 8, 16, 2, 6, 12, 6, 8, 4, 12, 24, 2, 6, 12, 6, 12, 6, 30, 24, 32, 4, 12, 36, 12, 16, 8, 16, 2, 6, 12, 6, 12, 6, 30, 24, 48, 6, 30, 60, 30, 24, 12, 60, 48, 4, 12, 36, 12, 36, 12, 60, 72, 64, 8, 24, 72, 24, 32, 64, 2, 6, 12, 6, 12, 6, 30, 24, 48, 6, 30, 60, 30, 24, 12, 60, 120, 6, 30, 60, 30, 60

Offset: 0

Antti Karttunen, Oct 05 2023

nonn

Antti Karttunen, Table of n, a(n) for n = 0..16384
Index entries for sequences related to binary expansion of n

Cf. A005940, A046523, A303767, A366260, A366262 (rgs-transform).

Cf. also A278219, A278222.

A046523(n) = { my(f=vecsort(factor(n)[,2],,4),p);prod(i=1,#f,(p=nextprime(p+1))^f[i]) }
A366261(n) = A046523(A366260(n)); \\ Needs also the program given in A366260.

a(n) = A046523(A366260(n)).
a(n) = A278222(A303767(n)).
A001222(a(n)) = A366254(n).

A286557 a(n) = A046523(A286555(n)).

Original entry on oeis.org

1, 2, 4, 2, 4, 8, 6, 2, 4, 12, 16, 6, 6, 12, 6, 2, 4, 12, 36, 6, 12, 32, 30, 6, 6, 30, 24, 6, 8, 12, 6, 2, 4, 12, 36, 12, 30, 72, 30, 8, 6, 60, 64, 6, 6, 60, 30, 6, 6, 30, 60, 6, 6, 48, 30, 6, 6, 24, 24, 6, 6, 12, 6, 2, 4, 12, 36, 6, 24, 72, 60, 6, 6, 210, 144, 6, 6, 60, 24, 6, 6, 30, 180, 6, 24, 128, 30, 6, 6, 30, 120, 6, 6, 60

Offset: 0

Antti Karttunen, May 13 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 0..8191

Cf. A003188, A046523, A278219, A286553, A286555.

(define (A286557 n) (A046523 (A286555 n)))

a(n) = A046523(A286555(n)).

a(n) = A286553(A003188(n)).

A286536 a(n) = A278222(A276445(n)).

Original entry on oeis.org

2, 4, 2, 4, 8, 2, 6, 4, 12, 8, 2, 16, 12, 6, 6, 4, 12, 12, 8, 2, 36, 32, 12, 24, 12, 6, 16, 30, 24, 6, 6, 4, 12, 12, 12, 8, 2, 36, 72, 32, 12, 60, 72, 12, 24, 12, 6, 36, 48, 30, 64, 48, 60, 24, 30, 24, 6, 16, 30, 60, 24, 6, 6, 4, 12, 12, 12, 12, 8, 2, 36, 72, 72, 32, 12, 60, 180, 72, 12, 60, 72, 12, 24, 12, 6, 36

Offset: 1

Antti Karttunen, May 17 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A267111, A276445, A278219, A278222, A286538.

Cf. A286537 (rgs-version of this sequence).

(define (A286536 n) (A278219 (A267111 n)))
(define (A286536 n) (A278222 (A276445 n)))

a(n) = A278222(A276445(n)).

a(n) = A278219(A267111(n)).

A304745 Restricted growth sequence transform of A046523(A207901(n)).

Original entry on oeis.org

1, 2, 3, 2, 4, 5, 6, 7, 4, 5, 8, 9, 3, 10, 3, 2, 3, 10, 11, 10, 12, 13, 8, 9, 4, 5, 8, 9, 3, 10, 3, 2, 4, 9, 8, 5, 14, 15, 14, 16, 17, 18, 19, 18, 8, 13, 12, 9, 4, 9, 8, 5, 14, 15, 14, 16, 20, 21, 22, 21, 6, 5, 4, 7, 4, 9, 8, 5, 14, 15, 14, 16, 17, 18, 19, 18, 8, 13, 12, 9, 12, 23, 24, 13, 25, 26, 25, 27, 17, 18, 19, 18, 8, 13, 12, 9, 3, 10, 11, 10, 12, 13, 8

Offset: 0

Antti Karttunen, May 27 2018

nonn

For all i, j: a(i) = a(j) => A005811(i) = A005811(j).

Antti Karttunen, Table of n, a(n) for n = 0..65537
Index entries for sequences related to binary expansion of n

Cf. A046523, A207901.

Cf. also A286619 (A278219), A304744.

up_to_e = 17; \\ Good for computing up to n = (2^up_to_e)-1
v050376 = vector(up_to_e);
ispow2(n) = (n && !bitand(n,n-1));
i = 0; for(n=1,oo,if(ispow2(isprimepower(n)), i++; v050376[i] = n); if(i == up_to_e,break));
A050376(n) = v050376[n];
A052330(n) = { my(p=1,i=1); while(n>0, if(n%2, p *= A050376(i)); i++; n >>= 1); (p); };
A003188(n) = bitxor(n, n>>1);
A207901(n) = A052330(A003188(n));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
v304745 = rgs_transform(vector(65538,n,A046523(A207901(n-1))));
A304745(n) = v304745[1+n];

A286580 a(n) = A278222(A233275(n)).

Original entry on oeis.org

1, 2, 4, 2, 4, 8, 6, 2, 4, 12, 8, 6, 16, 12, 6, 2, 4, 12, 12, 8, 36, 24, 6, 16, 30, 12, 6, 32, 24, 12, 6, 2, 4, 12, 12, 12, 36, 60, 8, 36, 24, 24, 6, 72, 72, 30, 16, 30, 48, 12, 6, 60, 60, 32, 24, 30, 12, 6, 64, 48, 24, 12, 6, 2, 4, 12, 12, 12, 36, 60, 12, 36, 60, 60, 8, 72, 180, 24, 36, 24, 180, 24, 6, 72, 120, 72, 72, 30, 30, 16

Offset: 0

Antti Karttunen, Jun 03 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 0..16383
Indranil Ghosh, Python program to generate the sequence

Cf. A233275, A278219, A278222, A286538, A286581 (rgs-version of this sequence).

(define (A286580 n) (A278222 (A233275 n)))

a(n) = A278222(A233275(n)).

cp's OEIS Frontend

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

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A366261 The least number with the same prime signature as A366260, where A366260 is Doudna sequence permuted by May code.

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A286557 a(n) = A046523(A286555(n)).

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A286536 a(n) = A278222(A276445(n)).

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A304745 Restricted growth sequence transform of A046523(A207901(n)).

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A286580 a(n) = A278222(A233275(n)).

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