A353522 Lexicographically earliest infinite sequence such that a(i) = a(j) => A000035(i) = A000035(j) and A003415(i) = A003415(j), for all i, j >= 1, where A000035 and A003415 compute the parity and the arithmetic derivative of their argument.

1, 2, 3, 4, 3, 5, 3, 6, 7, 8, 3, 9, 3, 10, 11, 12, 3, 13, 3, 14, 15, 16, 3, 17, 15, 18, 19, 12, 3, 20, 3, 21, 22, 23, 24, 25, 3, 13, 26, 27, 3, 28, 3, 29, 30, 31, 3, 32, 22, 33, 34, 35, 3, 36, 26, 37, 38, 20, 3, 37, 3, 39, 40, 41, 42, 43, 3, 44, 45, 46, 3, 47, 3, 48, 49, 21, 42, 50, 3, 51, 52, 53, 3, 54, 38, 33, 55, 56, 3, 57, 34, 58

Offset

1,2

Comments

Restricted growth sequence transform of the ordered pair [A000035(n), A003415(n)].

For all i, j:

A353520(i) = A353520(j) => A353521(i) = A353521(j) => a(i) = a(j).

Links

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

Prog

(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; };
A000035(n) = (n%2);
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
Aux353522(n) = [A000035(n), A003415(n)];
v353522 = rgs_transform(vector(up_to, n, Aux353522(n)));
A353522(n) = v353522[n];

Crossrefs

Cf. A000035, A003415.

Cf. also A305801, A353520, A353521.

Sequence in context: A352898 A318500 A325384 * A323371 A369447 A319346

Adjacent sequences: A353519 A353520 A353521 * A353523 A353524 A353525

Keyword

nonn

Author

Antti Karttunen, Apr 27 2022

Status

approved