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a(1)=1. Take the positive integers, then reverse the order of the integers a(m+1) through a(m+a(n)), where m = 1 + Sum_{k=1..n-1} a(k).
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%I #15 Sep 02 2024 19:32:54

%S 1,2,4,3,8,7,6,5,11,10,9,19,18,17,16,15,14,13,12,26,25,24,23,22,21,20,

%T 32,31,30,29,28,27,37,36,35,34,33,48,47,46,45,44,43,42,41,40,39,38,58,

%U 57,56,55,54,53,52,51,50,49,67,66,65,64,63,62,61,60,59,86,85,84,83,82

%N a(1)=1. Take the positive integers, then reverse the order of the integers a(m+1) through a(m+a(n)), where m = 1 + Sum_{k=1..n-1} a(k).

%C This sequence is a self-inverse permutation of the positive integers.

%H Rémy Sigrist, <a href="/A125566/b125566.txt">Table of n, a(n) for n = 1..10056</a>

%H Rémy Sigrist, <a href="/A125566/a125566.gp.txt">PARI program</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%e The sequence grouped by descending runs, where the n-th descending run, after the first 1, is made up of a(n) terms: 1, (2), (4, 3), (8, 7, 6, 5), (11, 10, 9), (19, 18, 17, 16, 15, 14, 13, 12), (26, 25, 24, 23, 22, 21, 20), (32, 31, 30, 29, 28, 27), (37, 36, 35, 34, 33), (48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38), ...

%o (PARI) \\ See Links section.

%Y Cf. A038722.

%K easy,nonn

%O 1,2

%A _Leroy Quet_, Jan 01 2007