A323236 Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j), where f(1) = 0, f(n) = -1 if n is an even number > 2, and f(n) = A323234(n) for odd numbers >= 3.

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

Offset: 1

Author

Antti Karttunen, Jan 08 2019

Keywords

• nonn

Comments

For all i, j:

A319702(i) = A319702(j) => a(i) = a(j),

A323234(i) = A323234(j) => a(i) = a(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A053645, A079944, A319702, A323234.

Cf. also A323242 (somewhat analogous filter sequence for prime factorization).

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; };
A053644(n) = { my(k=1); while(k<=n, k<<=1); (k>>1); }; \\ From A053644
A053645(n) = (n-A053644(n));
A079944off0(n) = (1==binary(2+n)[2]);
A323236aux(n) = if(1==n,0,if(!(n%2),-1,[A053645(n), A079944off0(n-2)]));
v323236 = rgs_transform(vector(up_to,n,A323236aux(n)));
A323236(n) = v323236[n];