A323235 Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j), where f(1) = 0, f(n) = -1 if n is an odd number > 1, and f(n) = A323234(n) for even numbers >= 4.

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

Offset: 1

Author

Antti Karttunen, Jan 08 2019

Keywords

• nonn

Comments

For all i, j:

A319701(i) = A319701(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, A319701, A323234.

Cf. also A323241 (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]);
A323235aux(n) = if(1==n,0,if(n%2,-1,[A053645(n), A079944off0(n-2)]));
v323235 = rgs_transform(vector(up_to,n,A323235aux(n)));
A323235(n) = v323235[n];