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Permutation of nonnegative integers: a(1) = 0, a(2) = 1, a(2n) = 2*a(n), a(2n+1) = 1 + 2*a( A269370(2n+1)).
+20
5
0, 1, 3, 2, 5, 6, 7, 4, 15, 10, 13, 12, 31, 14, 63, 8, 9, 30, 11, 20, 127, 26, 21, 24, 255, 62, 23, 28, 25, 126, 511, 16, 1023, 18, 29, 60, 2047, 22, 27, 40, 17, 254, 4095, 52, 47, 42, 61, 48, 8191, 510, 16383, 124, 41, 46, 95, 56, 55, 50, 53, 252, 19, 1022, 32767, 32, 49, 2046, 65535, 36, 131071, 58, 125, 120
COMMENTS
Note the indexing: Domain starts from 1, range from 0.
FORMULA
a(1) = 0, a(2) = 1, a(2n) = 2*a(n), a(2n+1) = 1 + 2*a( A269370(2n+1)). As a composition of related permutations:
PROG
(Scheme, with memoization-macro definec)
Permutation of natural numbers: a(1) = 0, after which a(2n) = 1 + 2*a(n), a(2n+1) = 2 * a( A269370(n)).
+20
4
0, 1, 2, 3, 6, 5, 4, 7, 8, 13, 10, 11, 16, 9, 32, 15, 14, 17, 12, 27, 64, 21, 26, 23, 128, 33, 24, 19, 22, 65, 256, 31, 512, 29, 18, 35, 1024, 25, 20, 55, 30, 129, 2048, 43, 48, 53, 34, 47, 4096, 257, 8192, 67, 54, 49, 96, 39, 40, 45, 42, 131, 28, 513, 16384, 63, 46, 1025, 32768, 59, 65536, 37, 66, 71, 131072, 2049, 262144, 51, 38, 41
COMMENTS
Note the indexing: Domain starts from 1, range from 0.
FORMULA
a(1) = 0, after which, a(2n) = 1 + 2*a(n), a(2n+1) = 2 * a( A269370(n)). As a composition of related permutations:
PROG
(Scheme, with memoization-macro definec)
Self-inverse permutation of natural numbers: a(1) = 1, for n even, a(n) = A269369(1+a(n/2)), for n odd, a(n) = 2*a( A269370(n)-1).
+20
4
1, 3, 2, 5, 4, 7, 6, 11, 14, 19, 8, 17, 22, 9, 34, 29, 12, 21, 10, 53, 18, 13, 28, 47, 106, 81, 42, 23, 16, 123, 94, 83, 246, 15, 44, 59, 166, 39, 38, 155, 68, 27, 118, 35, 162, 103, 24, 137, 54, 375, 274, 239, 20, 49, 70, 65, 78, 61, 36, 365, 58, 333, 750, 245, 56, 403, 666, 41, 806, 55, 212, 173, 82, 585, 346, 113, 84, 57, 1170, 461, 26, 73, 32
FORMULA
a(1) = 1, for n even, a(n) = A269369(1+a(n/2)), for n odd, a(n) = 2*a( A269370(n)-1).
PROG
(Scheme, with memoization-macro definec)
a(1) = 1, after which, for odd numbers: a(n) = A260739(n)-th number k for which A260738(k) = A260738(n)-1, and for even numbers: a(n) = a(n/2).
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14
1, 1, 2, 1, 3, 2, 5, 1, 4, 3, 7, 2, 11, 5, 6, 1, 13, 4, 9, 3, 8, 7, 17, 2, 23, 11, 10, 5, 25, 6, 19, 1, 12, 13, 15, 4, 29, 9, 14, 3, 37, 8, 41, 7, 16, 17, 43, 2, 21, 23, 18, 11, 47, 10, 31, 5, 20, 25, 35, 6, 53, 19, 22, 1, 27, 12, 61, 13, 24, 15, 67, 4, 55, 29, 26, 9, 71, 14, 33, 3, 28, 37, 77, 8, 49, 41, 30, 7, 83, 16, 89, 17, 32, 43, 39, 2
COMMENTS
For odd numbers n > 1, a(n) tells which term is on the immediately preceding row of A255127 (square array generated by Ludic sieve), in the same column where n itself is.
FORMULA
a(1) = 1; after which, for even numbers a(n) = a(n/2), and for odd numbers a(n) = A255127( A260738(n)-1, A260739(n)). Other identities. For all n >= 1:
1, 3, 7, 5, 19, 11, 9, 17, 13, 23, 39, 29, 15, 35, 21, 41, 61, 47, 27, 53, 25, 59, 81, 65, 31, 71, 45, 77, 103, 83, 33, 89, 37, 95, 123, 101, 43, 107, 57, 113, 145, 119, 49, 125, 55, 131, 165, 137, 51, 143, 63, 149, 187, 155, 85, 161, 97, 167, 207, 173, 91, 179, 67, 185, 229, 191, 69, 197, 73, 203, 249, 209, 75
COMMENTS
For n > 1, a(n) = the number located immediately below n in A255551 (square array generated by Lucky sieve) in the same column where n itself is. Permutation of odd numbers.
FORMULA
Other identities. For all n >= 1:
Permutation of natural numbers: a(1) = 1, a(2n) = 2*a(n), a( A269369(1+n)) = 1 + 2*a(n).
+10
4
1, 2, 3, 4, 7, 6, 5, 8, 13, 14, 15, 12, 17, 10, 25, 16, 11, 26, 9, 28, 21, 30, 27, 24, 57, 34, 53, 20, 31, 50, 49, 32, 101, 22, 35, 52, 65, 18, 29, 56, 51, 42, 105, 60, 69, 54, 23, 48, 85, 114, 97, 68, 19, 106, 121, 40, 37, 62, 43, 100, 33, 98, 229, 64, 55, 202, 197, 44, 405, 70, 115, 104, 89, 130, 209, 36, 107, 58, 261, 112, 61
FORMULA
a(1) = 1, after which for even n, a(n) = 2*a(n/2), for odd n, a(n) = 1 + 2*a( A269370(n)-1).
PROG
(Scheme, with memoization-macro definec)
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