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

%I A249814 #46 Dec 13 2015 07:47:37
%S A249814 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,
%T A249814 39,54,21,32,19,12,33,50,51,64,53,80,67,76,57,86,87,114,93,140,95,120,
%U A249814 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
%N A249814 "Mountains of Eratosthenes" permutation: a(1) = 1, a(n) = A249741(A001511(n), a(A003602(n))).
%C A249814 This sequence is a "recursed variant" of A249811.
%C A249814 From _Antti Karttunen_, Jan 18 2015: (Start)
%C A249814 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).
%C A249814 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:
%C A249814                                     1
%C A249814                                     |
%C A249814                  ...................2...................
%C A249814                 3                                       4
%C A249814       5......../ \........8                   7......../ \........6
%C A249814      / \                 / \                 / \                 / \
%C A249814     /   \               /   \               /   \               /   \
%C A249814    /     \             /     \             /     \             /     \
%C A249814   9       14         15       24         13       20         11       10
%C A249814 17 26   27  34     29  44   47  48     25  38   39  54     21  32   19  12
%C A249814 (End)
%C A249814 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
%H A249814 Antti Karttunen, <a href="/A249814/b249814.txt">Table of n, a(n) for n = 1..8191</a>
%H A249814 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A249814 In the following formulas, A083221 and A249741 are interpreted as bivariate functions:
%F A249814 a(1) = 1, for n>1: a(n) = A083221(A001511(n), a(A003602(n))) - 1 = A249741(A001511(n), a(A003602(n))).
%F A249814 a(1) = 1, a(2n) = A253886(a(n)), a(2n+1) = (2*a(n+1))-1. - _Antti Karttunen_, Jan 18 2015
%F A249814 As a composition of other permutations:
%F A249814 a(n) = A250244(A246684(n)).
%F A249814 Other identities. For all n >= 1, the following holds:
%F A249814 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.]
%F A249814 a(A000079(n-1)) = A006093(n).
%o A249814 (Scheme, with memoizing macro definec from _Antti Karttunen_'s IntSeq-library, two different implementations)
%o A249814 (definec (A249814 n) (cond ((<= n 1) n) (else (+ -1 (A083221bi (A001511 n) (A249814 (A003602 n))))))) ;; Code for A083221bi given in A083221.
%o A249814 (definec (A249814 n) (cond ((<= n 1) n) ((even? n) (A253886 (A249814 (/ n 2)))) (else (+ -1 (* 2 (A249814 (/ (+ n 1) 2)))))))
%Y A249814 Inverse: A249813.
%Y A249814 Similar or related permutations: A246684, A249811, A250244, A252755.
%Y A249814 Cf. A000079, A000265, A001511, A003602, A006093, A083140, A083221, A249741, A250469, A253886.
%Y A249814 Compare also the scatterplot of this sequence to the graphs of A252755 and A246684.
%Y A249814 Differs from A246684 for the first time at n=14, where a(14) = 20, while A246684(14) = 26.
%K A249814 nonn,tabf,look,hear
%O A249814 1,2
%A A249814 _Antti Karttunen_, Nov 06 2014