A291762 Restricted growth sequence transform of ((-1)^A000120(n))*A046523(n); filter combining the parity of binary weight with the prime signature of n.

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

Offset

1,2

Comments

Equally, restricted growth sequence transform of sequence b defined as b(1) = 1; b(n) = A046523(n) + A010060(n) for n > 1, which starts as 1, 3, 2, 5, 2, 6, 3, 9, 4, 6, 3, 12, 3, 7, 6, 17, 2, 12, 3, 12, 7, 7, ...

Links

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

Prog

(PARI)
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; };
write_to_bfile(start_offset, vec, bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
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
write_to_bfile(1, rgs_transform(vector(65537, n, ((-1)^hammingweight(n))*A046523(n))), "b291762_upto65537.txt");
\\ Or alternatively:
A010060(n) = (hammingweight(n)%2);
f(n) = if(1==n, n, A046523(n)+A010060(n));
write_to_bfile(1, rgs_transform(vector(16385, n, f(n))), "b291762.txt");

Crossrefs

Cf. A000120, A010060, A046523.

Cf. A101296, A286163, A291761 (related or similar filtering sequences).

Cf. A027697 (positions of 2's), A027699 (of 3's), A130593 (of 5's and 7's), A230095 (of 9's).

Cf. also A231431, A235001.

Sequence in context: A309255 A375290 A201443 * A235051 A322814 A324399

Adjacent sequences: A291759 A291760 A291761 * A291763 A291764 A291765

Keyword

nonn

Author

Antti Karttunen, Sep 11 2017

Status

approved