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A235491
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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.
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7
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0, 1, 4, 9, 2, 16, 7, 6, 25, 3, 61, 26, 17, 14, 13, 115, 5, 12, 359, 119, 67, 47, 43, 36, 791, 8, 11, 41, 3017, 81, 811, 407, 247, 227, 179, 7525, 23, 38, 37, 221, 34015, 27, 503, 22, 7765, 3509, 1943, 21, 1777, 1333, 93625, 97, 193, 146, 181, 1717, 486721, 121, 4493, 91, 96839, 10, 40217, 20813, 89
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OFFSET
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0,3
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COMMENTS
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The permutation is self-inverse (an involution), meaning that a(a(n)) = n for all n.
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LINKS
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FORMULA
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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.
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EXAMPLE
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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.
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.
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.
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PROG
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(Scheme, with memoization-macro definec from Antti Karttunen's IntSeq-library)
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CROSSREFS
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Cf. A236854 (a similar permutation constructed from prime and composite numbers).
Cf. A237126/A237427 (entanglement permutations between ludic/nonludic <-> odd/even numbers).
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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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