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Search: a082324 -id:a082324
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Permutation A057501 applied twice ("squared").
+10
11
0, 1, 2, 3, 4, 6, 8, 7, 5, 9, 11, 14, 16, 19, 21, 22, 18, 17, 20, 13, 12, 10, 15, 23, 25, 28, 30, 33, 37, 39, 42, 44, 47, 51, 53, 56, 60, 58, 59, 62, 63, 64, 49, 50, 46, 45, 48, 55, 54, 57, 61, 35, 36, 32, 31, 34, 27, 26, 24, 29, 41, 40, 38, 43, 52, 65, 67, 70, 72, 75
OFFSET
0,3
FORMULA
a(n) = A057501(A057501(n)).
CROSSREFS
Inverse of A082316. a(n) = A082313(A057164(n)). Occurs in A073200 as row 34359740687. Cf. also A082317-A082324.
Number of cycles: A054357. (In range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right).
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 17 2003, Proposed by Wouter Meeussen.
STATUS
approved
Permutation A057502 applied twice ("squared").
+10
7
0, 1, 2, 3, 4, 8, 5, 7, 6, 9, 21, 10, 20, 19, 11, 22, 12, 17, 16, 13, 18, 14, 15, 23, 58, 24, 57, 56, 25, 59, 26, 54, 53, 27, 55, 51, 52, 28, 62, 29, 61, 60, 30, 63, 31, 45, 44, 32, 46, 42, 43, 33, 64, 34, 48, 47, 35, 49, 37, 38, 36, 50, 39, 40, 41, 65, 170, 66, 169, 168
OFFSET
0,3
FORMULA
a(n) = A057502(A057502(n))
CROSSREFS
Inverse of A082315. a(n) = A057164(A082313(n)). Occurs in A073200 as row 549755978251. Cf. also A082317-A082324.
Number of cycles: A054357. (In range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right).
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 17 2003, Proposed by Wouter Meeussen.
STATUS
approved
Permutation A057501 applied thrice ("cubed").
+10
6
0, 1, 3, 2, 7, 5, 6, 4, 8, 17, 20, 12, 10, 15, 16, 19, 11, 9, 14, 22, 21, 18, 13, 45, 48, 54, 57, 61, 31, 34, 26, 24, 29, 40, 38, 43, 52, 44, 47, 53, 56, 60, 30, 33, 25, 23, 28, 39, 37, 42, 51, 63, 64, 59, 58, 62, 50, 49, 46, 55, 36, 35, 32, 27, 41, 129, 132, 138, 141, 145
OFFSET
0,3
FORMULA
a(n) = A057501(A082315(n))
CROSSREFS
Inverse of A082318. Occurs in A073200 as row 11150372599265311570767859136464952601119119. Cf. also A082319-A082324.
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 17 2003
STATUS
approved
Permutation A057501 applied five times ("^5").
+10
5
0, 1, 3, 2, 7, 6, 8, 4, 5, 17, 12, 16, 11, 22, 18, 13, 14, 9, 21, 15, 10, 20, 19, 45, 54, 31, 26, 40, 44, 53, 30, 25, 39, 63, 59, 50, 36, 46, 55, 32, 27, 41, 42, 51, 28, 23, 37, 62, 58, 49, 35, 43, 52, 29, 24, 38, 61, 57, 48, 34, 60, 56, 47, 33, 64, 129, 138, 157, 166, 180
OFFSET
0,3
FORMULA
a(n) = A082315(A082317(n))
CROSSREFS
Inverse of A082322. Occurs in A073200. Cf. also A082323-A082324.
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 17 2003
STATUS
approved
Permutation A057501 applied four times ("^4"), permutation A082315 squared.
+10
4
0, 1, 2, 3, 4, 8, 5, 7, 6, 9, 14, 21, 18, 13, 10, 15, 20, 17, 12, 19, 16, 11, 22, 23, 28, 37, 42, 51, 58, 62, 49, 46, 55, 35, 32, 27, 41, 24, 29, 38, 43, 52, 57, 61, 48, 45, 54, 34, 31, 26, 40, 56, 60, 47, 44, 53, 33, 30, 25, 39, 64, 63, 59, 50, 36, 65, 70, 79, 84, 93
OFFSET
0,3
FORMULA
a(n) = A082315(A082315(n))
CROSSREFS
Inverse of A082320. Occurs in A073200. Cf. also A082321-A082324.
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 17 2003
STATUS
approved
Permutation A057501 applied six times ("^6"), permutation A082317 squared, permutation A082315 cubed.
+10
4
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 21, 10, 20, 19, 11, 22, 12, 17, 16, 13, 18, 14, 15, 23, 37, 58, 49, 35, 24, 38, 57, 48, 34, 56, 47, 33, 64, 25, 39, 59, 50, 36, 26, 40, 54, 45, 31, 53, 44, 30, 63, 27, 41, 55, 46, 32, 51, 42, 28, 62, 52, 43, 29, 61, 60, 65, 79, 107, 121, 149
OFFSET
0,3
FORMULA
CROSSREFS
Inverse of A082324. a(n) = A057501(A082321(n)). Occurs in A073200.
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 17 2003
STATUS
approved
Permutation A057502 applied thrice ("cubed").
+10
3
0, 1, 3, 2, 7, 5, 6, 4, 8, 17, 12, 16, 11, 22, 18, 13, 14, 9, 21, 15, 10, 20, 19, 45, 31, 44, 30, 63, 46, 32, 42, 28, 62, 43, 29, 61, 60, 48, 34, 47, 33, 64, 49, 35, 37, 23, 58, 38, 24, 57, 56, 50, 36, 39, 25, 59, 40, 26, 54, 53, 41, 27, 55, 51, 52, 129, 87, 128, 86, 189
OFFSET
0,3
FORMULA
a(n) = A057502(A082316(n))
CROSSREFS
Inverse of A082317. Occurs in A073200 as row 730750818665451459101842418728548123849399632523. Cf. also A082319-A082324.
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 17 2003
STATUS
approved
Permutation A057502 applied five times ("^5").
+10
2
0, 1, 3, 2, 7, 8, 5, 4, 6, 17, 20, 12, 10, 15, 16, 19, 11, 9, 14, 22, 21, 18, 13, 45, 54, 31, 26, 40, 44, 53, 30, 25, 39, 63, 59, 50, 36, 46, 55, 32, 27, 41, 42, 51, 28, 23, 37, 62, 58, 49, 35, 43, 52, 29, 24, 38, 61, 57, 48, 34, 60, 56, 47, 33, 64, 129, 157, 87, 73, 115
OFFSET
0,3
FORMULA
a(n) = A082316(A082318(n))
CROSSREFS
Inverse of A082321. Occurs in A073200. Cf. also A082323-A082324.
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 17 2003
STATUS
approved
Permutation A057502 applied four times ("^4"), permutation A082316 squared.
+10
1
0, 1, 2, 3, 4, 6, 8, 7, 5, 9, 14, 21, 18, 13, 10, 15, 20, 17, 12, 19, 16, 11, 22, 23, 37, 58, 49, 35, 24, 38, 57, 48, 34, 56, 47, 33, 64, 25, 39, 59, 50, 36, 26, 40, 54, 45, 31, 53, 44, 30, 63, 27, 41, 55, 46, 32, 51, 42, 28, 62, 52, 43, 29, 61, 60, 65, 107, 170, 142, 100
OFFSET
0,3
FORMULA
a(n) = A082316(A082316(n))
CROSSREFS
Inverse of A082319. Occurs in A073200. Cf. also A082321-A082324.
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 17 2003
STATUS
approved

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