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

1,2

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

Prog

(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];

Crossrefs

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

Cf. also A305790.

Sequence in context: A329048 A167506 A305815 * A344568 A072813 A285106

Adjacent sequences: A305786 A305787 A305788 * A305790 A305791 A305792

Keyword

nonn

Author

Antti Karttunen, Jun 10 2018

Status

approved