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A266411
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a(1) = 1, after which each a(n) = (A004074(n)+1)-th number selected from those not yet in the sequence.
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5
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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
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listen;
history;
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internal format)
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OFFSET
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1,2
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LINKS
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MATHEMATICA
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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 *)
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PROG
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(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))))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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