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a(1) = 1, after which a(n) = n/2 for even n, and a(n) = a(1) = 1, a(2n) = A332819(n) for odd n.

For any node n >= 2 in binary trees like A332815, a(n) gives the parent node of n. (Here we assume that their initial root 1 is its own parent)..

Antti Karttunen, <a href="/A332893/b332893.txt">Table of n, a(n) for n = 1..65537</a>

MapFor any node n >= 2 in binary trees like x -> A332815, a(xn) movesgives the parent node of n. (Here we stepassume nearerthat totheir theinitial root in1 binaryis treesits likeown A332815.parent).

Cf. A332815, A332819, A332894.

Map x -> a(x) moves step nearer to the root in binary trees like A332815.

Cf. A332815, A332819.

allocated for Antti Karttunen

a(1) = 1, a(2n) = n, a(2n+1) = A332819(2n+1).

1, 1, 2, 2, 3, 3, 5, 4, 4, 5, 13, 6, 7, 7, 6, 8, 11, 9, 17, 10, 10, 11, 29, 12, 9, 13, 8, 14, 19, 15, 37, 16, 26, 17, 15, 18, 23, 19, 14, 20, 31, 21, 41, 22, 12, 23, 53, 24, 25, 25, 22, 26, 43, 27, 39, 28, 34, 29, 61, 30, 47, 31, 20, 32, 21, 33, 73, 34, 58, 35, 89, 36, 59, 37, 18, 38, 65, 39, 97, 40, 16, 41, 101, 42, 33, 43, 38, 44, 67, 45, 35

1,3

a(1) = 1, after which a(n) = n/2 for even n, and a(n) = a(1) = 1, a(2n) = A332819(n) for odd n.

(PARI)

A332819(n) = A108548(A064989(A332808(n)));

A332893(n) = if(1==n, n, if(!(n%2), n/2, A332819(n)));

Cf. A332819.

Cf. also A252463.

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Antti Karttunen, Mar 01 2020

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allocated for Antti Karttunen

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