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

Author

Antti Karttunen, Sep 11 2017

Keywords

• nonn

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

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.

Programs

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");