A291768 -id:A291768 - cp's OEIS frontend

A291761 Restricted growth sequence transform of ((-1)^n)*A046523(n); filter combining the parity and the prime signature of n.

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

Offset: 1

Antti Karttunen, Sep 11 2017

nonn

Equally, restricted growth sequence transform of sequence b defined as b(1) = 1, and for n > 1, b(n) = A046523(n) + A000035(n), which starts as 1, 2, 3, 4, 3, 6, 3, 8, 5, 6, 3, 12, 3, 6, 7, 16, 3, 12, 3, 12, ...

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

Cf. A291767, A291768 (bisections), A147516.
Cf. A046523, A101296, A286161, A286251, A286367, A291762 (related or similar filtering sequences).
Cf. A065091 (positions of 3's), A100484 (of 4 and 5's), A001248 (of 4 and 7's), A046388 (of 9's), A030078 (of 6 and 12's).
Cf. A098108 (one of the matching sequences).

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)^n)*A046523(n))),"b291761.txt");
\\ Or alternatively:
f(n) = if(1==n,n,A046523(n)+(n%2));
write_to_bfile(1,rgs_transform(vector(16385,n,f(n))),"b291761.txt");

A291767 Odd bisection of A291761.

Original entry on oeis.org

1, 3, 3, 3, 7, 3, 3, 9, 3, 3, 9, 3, 7, 12, 3, 3, 9, 9, 3, 9, 3, 3, 16, 3, 7, 9, 3, 9, 9, 3, 3, 16, 9, 3, 9, 3, 3, 16, 9, 3, 21, 3, 9, 9, 3, 9, 9, 9, 3, 16, 3, 3, 23, 3, 3, 9, 3, 9, 16, 9, 7, 9, 12, 3, 9, 3, 9, 26, 3, 3, 9, 9, 9, 16, 3, 3, 16, 9, 3, 9, 9, 3, 23, 3, 7, 16, 3, 16, 9, 3, 3, 9, 9, 9, 26, 3, 3, 23, 3, 3, 9, 9, 9, 16, 9

Offset: 1

Antti Karttunen, Sep 11 2017

nonn

Records occur at positions: 1, 2, 5, 8, 14, 23, 41, 53, 68, 113, 122, 158, 203, 338, 365, ... (= (A147516(n)+1)/2) that give also all distinct values in this sequence: 1, 3, 7, 9, 12, 16, 21, 23, 26, 32, 34, 37, 40, 46, 48, 53, 58, 59, 64, 69, 72, 77, 81, ... Note that the terms of A291768 are all from the complementary sequence: 2, 4, 5, 6, 8, 10, 11, 13, 14, 15, 17, ...

Antti Karttunen, Table of n, a(n) for n = 1..16385

Cf. A147516, A278223, A291761, A291768.

(define (A291767 n) (A291761 (+ n n -1)))

a(n) = A291761(2n - 1).

cp's OEIS Frontend

A291761 Restricted growth sequence transform of ((-1)^n)*A046523(n); filter combining the parity and the prime signature of n.

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