A235491 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.

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

Offset

0,3

Comments

The permutation is self-inverse (an involution), meaning that a(a(n)) = n for all n.

Links

Antti Karttunen, Table of n, a(n) for n = 0..74 (The terms after a(32) were computed with the help of 100000 term b-file uploaded by Donovan Johnson for A003309.)

Index entries for sequences that are permutations of the natural numbers

Formula

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.

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)))).

Example

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.

Prog

(Scheme, with memoization-macro definec from Antti Karttunen's IntSeq-library)
(definec (A235491 n) (cond ((< n 2) n) ((= 1 (A192490 n)) (A192607 (A235491 (- (A192512 n) 1)))) (else (A003309 (+ 1 (A235491 (A236863 n)))))))

Crossrefs

Cf. A236854 (a similar permutation constructed from prime and composite numbers).

Cf. A237126/A237427 (entanglement permutations between ludic/nonludic <-> odd/even numbers).

Cf. also A003309, A192607, A192490, A192512, A236863.

Sequence in context: A114578 A135044 A236854 * A256513 A358916 A064505

Adjacent sequences: A235488 A235489 A235490 * A235492 A235493 A235494

Keyword

nonn

Author

Antti Karttunen, Feb 07 2014

Status

approved