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A334866 a(0) = 1, and then after, a(2n) = a(n)^2, a(2n+1) = A334747(a(n)). 11
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
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
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).
PROG
(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))));
CROSSREFS
Cf. A334865 (inverse permutation), A334860 (mirror image).
Composition of permutations A005940 and A225546.
Cf. A001146 (left edge of the tree), A019565 (right edge), A334110 (the left children of the right edge).
Sequence in context: A366027 A114894 A183169 * A308317 A318363 A225546
KEYWORD
nonn,tabf
AUTHOR
Antti Karttunen, Jun 08 2020
STATUS
approved

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Last modified March 29 06:15 EDT 2024. Contains 371265 sequences. (Running on oeis4.)