A292603 Doudna-tree reduced modulo 4: a(n) = A005940(1+n) mod 4.

1, 2, 3, 0, 1, 2, 1, 0, 3, 2, 3, 0, 1, 2, 3, 0, 3, 2, 1, 0, 3, 2, 1, 0, 1, 2, 3, 0, 1, 2, 1, 0, 1, 2, 1, 0, 3, 2, 3, 0, 1, 2, 1, 0, 3, 2, 3, 0, 1, 2, 3, 0, 1, 2, 1, 0, 3, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 3, 0, 1, 2, 3, 0, 3, 2, 1, 0, 3, 2, 1, 0, 1, 2, 3, 0, 1, 2, 1, 0, 3, 2, 3, 0, 1, 2, 3, 0, 3, 2, 1, 0, 3, 2, 1, 0, 1

Offset: 0

Author

Antti Karttunen, Dec 01 2017

Keywords

• nonn

Examples

			The first six levels of the binary tree (compare also to the illustrations given at A005940 and A292602):
                               1
                               |
                               2
                ............../ \..............
               3                               0
        ....../ \......                 ....../ \......
       1               2               1               0
      / \             / \             / \             / \
     /   \           /   \           /   \           /   \
    3     2         3     0         1     2         3     0
   / \   / \       / \   / \       / \   / \       / \   / \
  3   2 1   0     3   2 1   0     1   2 3   0     1   2 1   0
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16383
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A003961, A005940, A292602.

Cf. A004767 (gives the positions of 0's), A016813 (of 2's).

Cf. also A246261, A246263, A246271, A292271, A292274, A292375, A292377, A292381, A292383, A292384, A292583.

Programs

Scheme

(define (A292603 n) (modulo (A005940 (+ 1 n)) 4))

Formula

a(n) = A010873(A005940(1+n)).

a(n) + 4*A292602(n) = A005940(1+n).

a(2n+1) = 2*a(n) mod 4.

a(A004767(n)) = 0.

a(A016813(n)) = 2.

a(2*A156552(A246261(n))) = 1.

a(2*A156552(A246263(n))) = 3.

a(n * 2^(1+A246271(A005940(1+n)))) = 1.