A332896 a(1) = 0, and for n > 1, a(n) = 2*a(A332893(n)) + [n == 3 (mod 4)].

0, 0, 1, 0, 2, 2, 5, 0, 0, 4, 21, 4, 10, 10, 5, 0, 42, 0, 85, 8, 8, 42, 341, 8, 0, 20, 1, 20, 170, 10, 1365, 0, 40, 84, 11, 0, 682, 170, 21, 16, 2730, 16, 5461, 84, 8, 682, 21845, 16, 0, 0, 85, 40, 10922, 2, 43, 40, 168, 340, 87381, 20, 43690, 2730, 17, 0, 16, 80, 349525, 168, 680, 22, 1398101, 0, 174762, 1364, 1, 340, 32, 42, 5592405, 32, 0, 5460

Offset: 1

Author

Antti Karttunen, Mar 04 2020

Keywords

• nonn

Comments

Base-2 expansion of a(n) encodes the steps where numbers of the form 4k+3 are encountered when map x -> A332893(x) is iterated down to 1, starting from x=n. See the binary tree illustrated in A332815.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A000975, A108546, A332815, A332893, A332895,

Cf. also A292383.

Programs

PARI

A332896(n) = if(1==n,n-1,2*A332896(A332893(n)) + (3==(n%4)));

Formula

a(1) = 0, and for n > 1, a(n) = 2*a(A332893(n)) + [n == 3 (mod 4)].

Other identities. For n >= 1:

a(2n) = 2*a(n).

a(A108546(n)) = A000975(n-1).