A305789 Filter-sequence combining prime signature of n (A046523) and similar signature for GF(2)[X]-factorization (A278233).

1, 2, 2, 3, 4, 5, 2, 6, 7, 8, 2, 9, 2, 5, 10, 11, 12, 13, 2, 14, 15, 5, 16, 17, 18, 5, 19, 9, 16, 20, 2, 21, 5, 22, 5, 23, 2, 5, 8, 24, 2, 25, 16, 9, 26, 27, 2, 28, 7, 29, 30, 9, 16, 31, 32, 17, 8, 27, 2, 33, 2, 5, 9, 34, 35, 36, 2, 37, 15, 36, 16, 38, 2, 5, 26, 9, 5, 39, 16, 40, 41, 5, 42, 43, 44, 27, 32, 17, 16, 45, 32, 46, 5, 5, 8, 47, 2, 13, 9, 48, 42

Offset: 1

Author

Antti Karttunen, Jun 10 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of ordered pair [A046523(n), A278233(n)].

For all i, j: a(i) = a(j) => A305802(i) = A305802(j).

Links

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

Crossrefs

Cf. A046523, A101296, A278233, A305788, A305802.

Cf. also A305790.

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; };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
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]); };
Aux305789(n) = [A046523(n), A278233(n)];
v305789 = rgs_transform(vector(up_to,n,Aux305789(n)));
A305789(n) = v305789[n];