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%I #17 Feb 10 2014 08:16:18
%S 0,1,4,9,2,16,7,6,25,3,61,26,17,14,13,115,5,12,359,119,67,47,43,36,
%T 791,8,11,41,3017,81,811,407,247,227,179,7525,23,38,37,221,34015,27,
%U 503,22,7765,3509,1943,21,1777,1333,93625,97,193,146,181,1717,486721,121,4493,91,96839,10,40217,20813,89
%N Self-inverse permutation of natural numbers: complementary pair ludic/nonludic numbers (A003309/A192607) entangled with the same pair in the opposite order, nonludic/ludic. See Formula.
%C The permutation is self-inverse (an involution), meaning that a(a(n)) = n for all n.
%H Antti Karttunen, <a href="/A235491/b235491.txt">Table of n, a(n) for n = 0..74</a> (The terms after a(32) were computed with the help of 100000 term b-file uploaded by Donovan Johnson for A003309.)
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F a(0)=0, a(1)=1, and for n > 1, if n is k-th ludic number (i.e., n = A003309(k)), then a(n) = nonludic(a(k-1)); otherwise, when n is k-th nonludic number (i.e., n = A192607(k)), then a(n) = ludic(a(k)+1), where ludic numbers are given by A003309, and nonludic numbers by A192607.
%F a(0)=0, a(1)=1, and for n > 1, if A192490(n)=1 (n is ludic) a(n) = A192607(a(A192512(n)-1)); otherwise (n is nonludic), a(n) = A003309(1+(a(A236863(n)))).
%e For n=2, with 2 being the second ludic number (= A003309(4)), the value is computed as nonludic(a(2-1)) = nonludic(a(1)) = 4, the first nonludic number, thus a(2) = 4.
%e For n=5, with 5 being the fourth ludic number (= A003309(4)), the value is computed as nonludic(a(4-1)) = nonludic(a(3)) = nonludic(9) = 16, thus a(5) = 16.
%e For n=6, with 6 being the second nonludic number (= A192607(2)), the value is computed as ludic(a(2)+1) = ludic(4+1) = ludic(5) = 7, thus a(6) = 7.
%o (Scheme, with memoization-macro definec from _Antti Karttunen_'s IntSeq-library)
%o (definec (A235491 n) (cond ((< n 2) n) ((= 1 (A192490 n)) (A192607 (A235491 (- (A192512 n) 1)))) (else (A003309 (+ 1 (A235491 (A236863 n)))))))
%Y Cf. A236854 (a similar permutation constructed from prime and composite numbers).
%Y Cf. A237126/A237427 (entanglement permutations between ludic/nonludic <-> odd/even numbers).
%Y Cf. also A003309, A192607, A192490, A192512, A236863.
%K nonn
%O 0,3
%A _Antti Karttunen_, Feb 07 2014
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