A334866 a(0) = 1, and then after, a(2n) = a(n)^2, a(2n+1) = A334747(a(n)).

1, 2, 4, 3, 16, 8, 9, 6, 256, 32, 64, 12, 81, 18, 36, 5, 65536, 512, 1024, 48, 4096, 128, 144, 24, 6561, 162, 324, 27, 1296, 72, 25, 10, 4294967296, 131072, 262144, 768, 1048576, 2048, 2304, 96, 16777216, 8192, 16384, 192, 20736, 288, 576, 20, 43046721, 13122, 26244, 243, 104976, 648, 729, 54, 1679616, 2592, 5184, 108, 625, 50, 100, 15

Offset: 0

Author

Antti Karttunen, Jun 08 2020

Keywords

• nonn
• tabf

Comments

This irregular table can be represented as a binary tree. Each child to the left is obtained by squaring the parent, and each child to the right is obtained by applying A334747 to the parent:

1

|

...................2...................

4 3

16......../ \........8 9......../ \........6

/ \ / \ / \ / \

/ \ / \ / \ / \

/ \ / \ / \ / \

256 32 64 12 81 18 36 5

65536 512 1024 48 4096 128 144 24 6561 162 324 27 1296 72 25 10

etc.

This is the mirror image of the tree in A334860.

Links

• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A334865 (inverse permutation), A334860 (mirror image).

Composition of permutations A005940 and A225546.

Cf. A000290, A048675, A087808, A334747, A334870.

Cf. A001146 (left edge of the tree), A019565 (right edge), A334110 (the left children of the right edge).

Programs

PARI

A334747(n) = { my(c=core(n), m=n); forprime(p=2, , if(c % p, m*=p; break, m/=p)); m; }; \\ From A334747
A334866(n) = if(!n,1,if(!(n%2),A334866(n/2)^2,A334747(A334866((n-1)/2))));

Formula

a(0) = 1, and then after, a(2n) = a(n)^2, a(2n+1) = A334747(a(n)).

a(n) = A225546(A005940(1+n)).

For all n >= 0, A048675(a(n)) = A087808(n).