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a(1) = 1, after which each a(n) = A002487(n)-th number selected from those not yet in the sequence.
3

%I #8 Jan 02 2016 04:15:00

%S 1,2,4,3,7,6,9,5,12,11,15,10,17,14,18,8,21,20,25,19,28,24,29,16,31,27,

%T 34,23,35,30,33,13,38,37,43,36,47,42,48,32,51,46,55,41,56,49,53,26,57,

%U 52,62,45,65,59,64,40,66,60,69,50,68,58,63,22,71,70,77,67,82,76,83,61,87,81,92,75,93,84,89,54,94,88,101,80

%N a(1) = 1, after which each a(n) = A002487(n)-th number selected from those not yet in the sequence.

%H Antti Karttunen, <a href="/A266413/b266413.txt">Table of n, a(n) for n = 1..16385</a>

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

%t f[n_] := Block[{a = {1}, g, b = Range[2, n]}, g[1] = 1; g[x_] := g[x] = If[EvenQ@ x, g[x/2], g[(x - 1)/2] + g[(x + 1)/2]]; Do[{AppendTo[a, #[[1, 1]]], Set[b, Last@ #]} &@ If[# > Length@ b, Break[], TakeDrop[b, {#}]] &@ g@ k, {k, 2, n}]; a]; f@ 103 (* _Michael De Vlieger_, Dec 29 2015, Version 10.2, after _N. J. A. Sloane_ at A002487 *)

%o (Scheme, with defineperm1-macro from Antti Karttunen's IntSeq-library)

%o (defineperm1 (A266413 n) (if (<= n 1) n (let loop ((i 1) (the-nth-one (+ -1 (A002487 n)))) (cond ((not-lte? (A266414 i) n) (if (zero? the-nth-one) i (loop (+ i 1) (- the-nth-one 1)))) (else (loop (+ i 1) the-nth-one))))))

%o (define (A266414 n) (A266413 (- n))) ;; This returns inverse values of A266413 from its hidden cache that defineperm1-macro has prepared. #f is returned for those n that have not yet been encountered.

%o ;; We consider a > b (i.e. not less than b) also in case a is #f.

%o ;; (Because of the stateful caching system used by defineperm1-macro):

%o (define (not-lte? a b) (cond ((not (number? a)) #t) (else (> a b))))

%Y Inverse: A266414.

%Y Cf. A002487.

%Y Similar permutations in Quetian style: A119435, A126917, A246165, A266411.

%Y Cf. also A266405.

%K nonn

%O 1,2

%A _Antti Karttunen_, Dec 29 2015