A336152 Lexicographically earliest infinite sequence such that a(i) = a(j) => A001221(i) = A001221(j) and A007814(1+i) = A007814(1+j), for all i, j >= 1.

1, 2, 3, 2, 4, 5, 6, 2, 4, 5, 3, 5, 4, 5, 7, 2, 4, 5, 3, 5, 8, 5, 6, 5, 4, 5, 3, 5, 4, 9, 10, 2, 8, 5, 11, 5, 4, 5, 12, 5, 4, 9, 3, 5, 8, 5, 13, 5, 4, 5, 11, 5, 4, 5, 12, 5, 8, 5, 3, 9, 4, 5, 14, 2, 8, 9, 3, 5, 8, 9, 6, 5, 4, 5, 11, 5, 8, 9, 13, 5, 4, 5, 3, 9, 8, 5, 12, 5, 4, 9, 11, 5, 8, 5, 15, 5, 4, 5, 11, 5, 4, 9, 6, 5, 16

Offset: 1

Author

Antti Karttunen, Jul 11 2020

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A001221(n), A007814(1+n)]. The first member of pair gives the number of distinct prime divisors of n, and the second member gives the number of trailing 1-bits in its binary expansion.

For all i, j: A324400(i) = A324400(j) => a(i) = a(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A001221, A007814.

Cf. also A324400, A336150, A336151, A336156.

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; };
A007814(n) = valuation(n,2);
Aux336152(n) = [omega(n), A007814(1+n)];
v336152 = rgs_transform(vector(up_to, n, Aux336152(n)));
A336152(n) = v336152[n];