A252755 - OEIS

A252755

Tree of Eratosthenes, mirrored: a(0) = 1, a(1) = 2; after which, a(2n) = 2*a(n), a(2n+1) = A250469(a(n)).

1, 2, 4, 3, 8, 9, 6, 5, 16, 21, 18, 25, 12, 15, 10, 7, 32, 45, 42, 55, 36, 51, 50, 49, 24, 33, 30, 35, 20, 27, 14, 11, 64, 93, 90, 115, 84, 123, 110, 91, 72, 105, 102, 125, 100, 147, 98, 121, 48, 69, 66, 85, 60, 87, 70, 77, 40, 57, 54, 65, 28, 39, 22, 13, 128, 189, 186, 235, 180, 267, 230, 203, 168, 249, 246, 305, 220, 327, 182, 187, 144

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OFFSET

0,2

COMMENTS

This sequence can be represented as a binary tree. Each child to the left is obtained by doubling the parent, and each child to the right is obtained by applying A250469 to the parent:

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

4 3

8......../ \........9 6......../ \........5

/ \ / \ / \ / \

16 21 18 25 12 15 10 7

32 45 42 55 36 51 50 49 24 33 30 35 20 27 14 11

etc.

Sequence A252753 is the mirror image of the same tree. A253555(n) gives the distance of n from 1 in both trees.

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..8192

Antti Karttunen, Entanglement Permutations, 2016-2017

Index entries for sequences that are permutations of the natural numbers

FORMULA

a(0) = 1, a(1) = 2; after which, a(2n) = 2*a(n), a(2n+1) = A250469(a(n)).

As a composition of related permutations:

a(n) = A252753(A054429(n)).

a(n) = A250245(A163511(n)).

MATHEMATICA

(* b = A250469 *) b[1] = 1; b[n_] := If[PrimeQ[n], NextPrime[n], m1 = p1 = FactorInteger[n][[1, 1]]; For[k1 = 1, m1 <= n, m1 += p1; If[m1 == n, Break[]]; If[FactorInteger[m1][[1, 1]] == p1, k1++]]; m2 = p2 = NextPrime[p1]; For[k2 = 1, True, m2 += p2, If[FactorInteger[m2][[1, 1]] == p2, k2++]; If[k1 + 2 == k2, Return[m2]]]];

a[0] = 1; a[1] = 2; a[n_] := a[n] = If[EvenQ[n], 2 a[n/2], b[a[(n-1)/2]]];

Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Mar 08 2016 *)

PROG

(Scheme, with memoization-macro definec)

(definec (A252755 n) (cond ((<= n 1) (+ n 1)) ((even? n) (* 2 (A252755 (/ n 2)))) (else (A250469 (A252755 (/ (- n 1) 2))))))

CROSSREFS

Inverse: A252756.

Row sums: A253787, products: A253788.

Similar permutations: A163511, A252753, A054429, A163511, A250245, A269865.

Cf. also: A249814 (Compare the scatterplots).

Cf. A083221, A250469, A253555.

Sequence in context: A365656 A182944 A269385 * A366275 A163511 A332817