A325561 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j) where f(n) = A234741(n) except for those numbers for which A234741(n) = n, in which case f(n) = 0.

1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 4, 1, 1, 1, 5, 1, 6, 1, 1, 1, 1, 1, 7, 1, 8, 9, 1, 1, 10, 1, 1, 11, 1, 1, 5, 1, 1, 1, 12, 13, 1, 1, 1, 14, 15, 1, 16, 1, 1, 1, 1, 1, 8, 1, 17, 18, 1, 1, 17, 19, 1, 20, 1, 1, 21, 1, 22, 23, 1, 1, 5, 1, 1, 24, 1, 1, 15, 1, 1, 13, 25, 1, 26, 1, 1, 1, 1, 27, 15, 28, 1, 1, 1, 1, 29

Offset: 1

Author

Antti Karttunen, May 10 2019

Keywords

• nonn

Comments

For all i, j:

A305801(i) = A305801(j) => a(i) = a(j) => A325562(i) = A325562(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to polynomials in ring GF(2)[X]

Crossrefs

Cf. A234741, A305801, A325562.

Programs

PARI

up_to = 65537;
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; };
A234741(n) = {n=factor(n); n[, 1]=apply(t->Pol(binary(t)), n[, 1]); sum(i=1, #n=Vec(factorback(n))%2, n[i]<<(#n-i))}; \\ From A234741
Aux325561(n) = { my(u=A234741(n)); if(u==n,0,u); };
v325561 = rgs_transform(vector(up_to,n,Aux325561(n)));
A325561(n) = v325561[n];