A305788 Restricted growth sequence transform of A278233, filter-sequence for GF(2)[X]-factorization.

1, 2, 2, 3, 3, 4, 2, 5, 4, 6, 2, 6, 2, 4, 5, 7, 7, 8, 2, 9, 3, 4, 4, 10, 2, 4, 6, 6, 4, 10, 2, 11, 4, 12, 4, 13, 2, 4, 6, 14, 2, 6, 4, 6, 10, 8, 2, 12, 4, 4, 11, 6, 4, 13, 2, 10, 6, 8, 2, 14, 2, 4, 6, 15, 9, 8, 2, 16, 3, 8, 4, 17, 2, 4, 10, 6, 4, 13, 4, 16, 3, 4, 8, 9, 15, 8, 2, 10, 4, 17, 2, 13, 4, 4, 6, 18, 2, 8, 6, 6, 8, 18, 2, 10, 10

Offset: 1

Author

Antti Karttunen, Jun 10 2018

Keywords

• nonn

Comments

This is GF(2)[X] analog of A101296.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences operating on GF(2)[X]-polynomials

Crossrefs

Cf. A278233.

Cf. A014580 (positions of 2's).

Cf. also A101296, A304529, A304751, A305789.

Programs

PARI

up_to = 65537;
rgs_transform(invec) = { my(occurrences = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(occurrences,invec[i]), my(pp = mapget(occurrences, invec[i])); outvec[i] = outvec[pp] , mapput(occurrences,invec[i],i); outvec[i] = u; u++ )); outvec; };
A278233(n) = { my(p=0, f=vecsort((factor(Pol(binary(n))*Mod(1, 2))[, 2]), , 4)); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };
v305788 = rgs_transform(vector(up_to,n,A278233(n)));
A305788(n) = v305788[n];