A336126 Lexicographically earliest infinite sequence such that a(i) = a(j) => A000035(i) = A000035(j) and A007814(1+A000265(i)) = A007814(1+A000265(j)), for all i, j >= 1.

1, 2, 3, 2, 1, 4, 5, 2, 1, 2, 3, 4, 1, 6, 7, 2, 1, 2, 3, 2, 1, 4, 5, 4, 1, 2, 3, 6, 1, 8, 9, 2, 1, 2, 3, 2, 1, 4, 5, 2, 1, 2, 3, 4, 1, 6, 7, 4, 1, 2, 3, 2, 1, 4, 5, 6, 1, 2, 3, 8, 1, 10, 11, 2, 1, 2, 3, 2, 1, 4, 5, 2, 1, 2, 3, 4, 1, 6, 7, 2, 1, 2, 3, 2, 1, 4, 5, 4, 1, 2, 3, 6, 1, 8, 9, 4, 1, 2, 3, 2, 1, 4, 5, 2, 1

Offset: 1

Author

Antti Karttunen, Jul 13 2020

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A000035(n), A007814(1+A000265(n))], parity and the number of trailing 1-bits in the odd part of n (i.e., the length of the rightmost run of 1-bits in its binary expansion).

For all i, j: A336146(i) = A336146(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. A000265, A007814, A336146.

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; };
A000265(n) = (n>>valuation(n,2));
A007814(n) = valuation(n,2);
Aux336126(n) = [(n%2),A007814(1+A000265(n))];
v336126 = rgs_transform(vector(up_to, n, Aux336126(n)));
A336126(n) = v336126[n];