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 A237126 a(0)=0, a(1) = 1, a(2n) = nonludic(a(n)), a(2n+1) = ludic(a(n)+1), where ludic = A003309, nonludic = A192607. 25
 0, 1, 4, 2, 9, 7, 6, 3, 16, 25, 14, 17, 12, 13, 8, 5, 26, 61, 36, 115, 22, 47, 27, 67, 20, 41, 21, 43, 15, 23, 10, 11, 38, 119, 81, 359, 51, 179, 146, 791, 33, 91, 64, 247, 39, 121, 88, 407, 31, 83, 57, 221, 32, 89, 59, 227, 24, 53, 34, 97, 18, 29, 19, 37, 54 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Shares with permutation A237056 the property that the other bisection consists of only ludic numbers and the other bisection of only nonludic numbers. However, instead of placing terms in those subsets in monotone order this sequence recursively permutes the order of both subsets with the emerging permutation itself, so this is a kind of "deep" variant of A237056. Alternatively, this can be viewed as yet another "entanglement permutation", where two pairs of complementary subsets of natural numbers are entangled with each other. In this case a complementary pair odd/even numbers (A005408/A005843) is entangled with a complementary pair ludic/nonludic numbers (A003309/A192607). LINKS Antti Karttunen, Table of n, a(n) for n = 0..574 FORMULA a(0)=0, a(1) = 1, a(2n) = nonludic(a(n)), a(2n+1) = ludic(a(n)+1), where ludic = A003309, nonludic = A192607. EXAMPLE a(2) = a(2*1) = nonludic(a(1)) = A192607(1) = 4. a(3) = a(2*1+1) = ludic(a(1)+1) = A003309(1+1) = A003309(2) = 2. a(4) = a(2*2) = nonludic(a(2)) = A192607(4) = 9. a(5) = a(2*2+1) = ludic(a(2)+1) = A003309(4+1) = A003309(5) = 7. PROG (Haskell) import Data.List (transpose) a237126 n = a237126_list !! n a237126_list = 0 : es where    es = 1 : concat (transpose [map a192607 es, map (a003309 . (+ 1)) es]) -- Reinhard Zumkeller, Feb 10 2014, Feb 06 2014 (Scheme, with Antti Karttunen's IntSeq-library for memoizing definec-macro) (definec (A237126 n) (cond ((< n 2) n) ((even? n) (A192607 (A237126 (/ n 2)))) (else (A003309 (+ 1 (A237126 (/ (- n 1) 2))))))) ;; Antti Karttunen, Feb 07 2014 CROSSREFS Cf. A237427 (inverse), A237056, A235491. Similarly constructed permutations: A227413/A135141. Sequence in context: A257730 A246378 A260422 * A246380 A200639 A243968 Adjacent sequences:  A237123 A237124 A237125 * A237127 A237128 A237129 KEYWORD nonn AUTHOR Antti Karttunen and Reinhard Zumkeller, Feb 06 2014 STATUS approved

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Last modified April 12 15:00 EDT 2021. Contains 342921 sequences. (Running on oeis4.)