A305790 Filter-sequence combining prime signature of n (A046523) and similar signature obtained when (0,1)-polynomial encoded in the binary expansion of n is factored over Q (A304751).

1, 2, 2, 3, 2, 4, 2, 5, 6, 4, 2, 7, 2, 4, 4, 8, 2, 9, 2, 7, 4, 4, 2, 10, 11, 4, 12, 7, 2, 13, 2, 14, 4, 4, 4, 15, 2, 4, 4, 10, 2, 13, 2, 7, 9, 4, 2, 16, 6, 17, 4, 7, 2, 18, 19, 10, 4, 4, 2, 20, 2, 4, 9, 21, 4, 13, 2, 7, 19, 13, 2, 22, 2, 4, 9, 7, 19, 13, 2, 16, 23, 4, 2, 20, 4, 4, 19, 10, 2, 24, 19, 7, 4, 4, 4, 25, 2, 9, 7, 26, 2, 13, 2, 10, 13

Offset: 1

Author

Antti Karttunen, Jun 10 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of ordered pair [A046523(n), A304751(n)].

For all i, j: a(i) = a(j) => A305821(i) = A305821(j).

Links

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

Crossrefs

Cf. A046523, A101296, A304751, A305821.

Cf. also 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; };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
Aux304751(n) = { my(p=0, f=vecsort((factor(Pol(binary(n)))[, 2]), , 4)); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }
Aux305790(n) = [A046523(n), Aux304751(n)];
v305790 = rgs_transform(vector(up_to,n,Aux305790(n)));
A305790(n) = v305790[n];