A249814 "Mountains of Eratosthenes" permutation: a(1) = 1, a(n) = A249741(A001511(n), a(A003602(n))).

1, 2, 3, 4, 5, 8, 7, 6, 9, 14, 15, 24, 13, 20, 11, 10, 17, 26, 27, 34, 29, 44, 47, 48, 25, 38, 39, 54, 21, 32, 19, 12, 33, 50, 51, 64, 53, 80, 67, 76, 57, 86, 87, 114, 93, 140, 95, 120, 49, 74, 75, 94, 77, 116, 107, 90, 41, 62, 63, 84, 37, 56, 23, 16, 65, 98, 99, 124, 101, 152, 127, 118, 105, 158, 159, 204, 133, 200, 151, 142

Offset: 1

Author

Antti Karttunen, Nov 06 2014

Keywords

• nonn
• tabf
• look
• hear

Comments

This sequence is a "recursed variant" of A249811.

From Antti Karttunen, Jan 18 2015: (Start)

This can be viewed as an entanglement or encoding permutation where the complementary pairs of sequences to be interwoven together are even and odd numbers (A005843/A005408) which are entangled with another complementary pair: even numbers in the order they appear in A253886 and odd numbers in their usual order: (A253886/A005408).

From the above follows also that this sequence can be represented as a binary tree. Each child to the left is obtained by doubling the parent and subtracting one, and each child to the right is obtained by applying A253886 to the parent:

1

|

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

3 4

5......../ \........8 7......../ \........6

/ \ / \ / \ / \

/ \ / \ / \ / \

/ \ / \ / \ / \

9 14 15 24 13 20 11 10

17 26 27 34 29 44 47 48 25 38 39 54 21 32 19 12

(End)

For listening I recommend some (mostly) percussive MIDI-instrument and the pitch offset set to at least 29 and the tempo (rate) to about 60. - Antti Karttunen, Feb 17 2015

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8191
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A249813.

Similar or related permutations: A246684, A249811, A250244, A252755.

Cf. A000079, A000265, A001511, A003602, A006093, A083140, A083221, A249741, A250469, A253886.

Compare also the scatterplot of this sequence to the graphs of A252755 and A246684.

Differs from A246684 for the first time at n=14, where a(14) = 20, while A246684(14) = 26.

Formula

In the following formulas, A083221 and A249741 are interpreted as bivariate functions:

a(1) = 1, for n>1: a(n) = A083221(A001511(n), a(A003602(n))) - 1 = A249741(A001511(n), a(A003602(n))).

a(1) = 1, a(2n) = A253886(a(n)), a(2n+1) = (2*a(n+1))-1. - Antti Karttunen, Jan 18 2015

As a composition of other permutations:

a(n) = A250244(A246684(n)).

Other identities. For all n >= 1, the following holds:

a(n) = (1+a((2*n)-1))/2. [The odd bisection from a(1) onward with one added and then halved gives the sequence back.]

a(A000079(n-1)) = A006093(n).