A266411 - OEIS

%I #9 Jan 02 2016 04:14:43

%S 1,2,4,3,6,8,7,5,10,12,14,13,16,15,11,9,18,20,22,24,23,26,28,27,30,29,

%T 25,32,31,21,19,17,34,36,38,40,42,41,44,46,48,47,50,52,51,54,53,49,56,

%U 58,57,60,59,55,62,61,45,43,64,63,39,37,35,33,66,68,70,72,74,76,75,78,80,82,84,83,86,88,90,89,92,94,93,96,95,91

%N a(1) = 1, after which each a(n) = (A004074(n)+1)-th number selected from those not yet in the sequence.

%H Antti Karttunen, <a href="/A266411/b266411.txt">Table of n, a(n) for n = 1..8192</a>

%H <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</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] = g[2] = 1; g[x_] := g[x] = g[g[x - 1]] + g[x - g[x - 1]]; Do[{AppendTo[a, #[[1, 1]]], Set[b, Last@ #]} &@ If[# > Length@ b, Break[], TakeDrop[b, {#}]] &@ (2 g[#] - # + 1) &@ k, {k, 2, n}]; a]; f@ 97 (* _Michael De Vlieger_, Dec 29 2015, Version 10.2, based on _Harvey P. Dale_ at A004074 *)

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

%o (defineperm1 (A266411 n) (if (<= n 1) n (let loop ((i 1) (the-nth-one (A004074 n))) (cond ((not-lte? (A266412 i) n) (if (zero? the-nth-one) i (loop (+ i 1) (- the-nth-one 1)))) (else (loop (+ i 1) the-nth-one))))))

%o (define (A266412 n) (A266411 (- n))) ;; This returns inverse values of A266411 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: A266412.

%Y Cf. A004074.

%Y Similar permutations in Quetian style: A119435, A126917, A246165, A266413.

%Y Cf. also A265901, A265903.

%K nonn

%O 1,2

%A _Antti Karttunen_, Dec 29 2015