A266411 a(1) = 1, after which each a(n) = (A004074(n)+1)-th number selected from those not yet in the sequence.

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

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..8192

Index entries for Hofstadter-type sequences

Index entries for sequences that are permutations of the natural numbers

Mathematica

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 *)

Prog

(Scheme, with defineperm1-macro from Antti Karttunen's IntSeq-library)
(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))))))
(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.
;; We consider a > b (i.e. not less than b) also in case a is #f.
;; (Because of the stateful caching system used by defineperm1-macro):
(define (not-lte? a b) (cond ((not (number? a)) #t) (else (> a b))))

Crossrefs

Inverse: A266412.

Cf. A004074.

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

Cf. also A265901, A265903.

Sequence in context: A280864 A364884 A369825 * A264740 A349370 A137621

Adjacent sequences: A266408 A266409 A266410 * A266412 A266413 A266414

Keyword

nonn

Author

Antti Karttunen, Dec 29 2015

Status

approved