A324532 Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A000120(n), A318458(n)] for all other numbers, except f(1) = 0.

1, 2, 3, 2, 3, 4, 5, 2, 6, 7, 5, 6, 5, 8, 9, 2, 3, 10, 5, 11, 5, 12, 13, 6, 14, 15, 9, 16, 13, 17, 18, 2, 3, 6, 5, 19, 5, 12, 13, 20, 5, 21, 13, 22, 23, 17, 18, 6, 14, 21, 24, 25, 13, 26, 27, 14, 24, 28, 18, 29, 18, 30, 31, 2, 3, 32, 5, 6, 5, 33, 13, 34, 5, 35, 13, 36, 13, 37, 18, 38, 14, 14, 13, 39, 40, 41, 18, 42, 13, 43, 27, 44, 18, 45, 46, 6, 5, 36, 23, 47, 13

Offset: 1

Author

Antti Karttunen, Mar 05 2019

Keywords

• nonn

Links

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

Crossrefs

Cf. A000120, A318458, A324530, A324531.

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; };
A318458(n) = bitand(n,sigma(n)-n);
Aux324532(n) = if(1==n,0,[hammingweight(n), A318458(n)]);
v324532 = rgs_transform(vector(up_to,n,Aux324532(n)));
A324532(n) = v324532[n];

Formula

For n >= 1, a(2^n) = 2.