A273668 -id:A273668 - cp's OEIS frontend

A275838 Permutation of nonnegative integers: a(n) = A273668(A225901(n)).

0, 1, 2, 9, 3, 5, 6, 57, 32, 33, 19, 20, 8, 17, 14, 23, 41, 13, 4, 15, 11, 29, 7, 21, 24, 133, 272, 47, 293, 70, 150, 263, 152, 357, 109, 110, 74, 68, 78, 163, 69, 73, 135, 545, 249, 58, 230, 220, 30, 37, 62, 225, 100, 161, 54, 127, 86, 285, 209, 85, 182, 172, 50, 51, 197, 42, 104, 231, 105, 431, 52, 35, 12, 43, 56, 99, 213, 95, 38, 25, 134, 153, 81, 341, 26, 76

Offset: 0

Antti Karttunen, Aug 13 2016

Inverse: A275837.
Cf. A225901, A273668, A153880, A266193, A273670, A275842.
Cf. A275839 (fixed points).
Cf. also A275835, A275836.

(define (A275838 n) (A273668 (A225901 n)))

a(n) = A273668(A225901(n)).
Other identities. For all n >= 0:
a(n) = A266193(a(A153880(n))). [Restriction to A153880 induces the same permutation.]
A275842(n) = A273663(a(A273670(n))). [While restriction to A273670 induces another permutation.]

A275836 Permutation of nonnegative integers: a(n) = A225901(A273668(n)).

Original entry on oeis.org

0, 1, 5, 3, 4, 23, 2, 17, 19, 11, 21, 99, 22, 15, 111, 13, 16, 9, 18, 95, 7, 10, 118, 119, 20, 51, 101, 98, 106, 107, 14, 27, 113, 110, 85, 89, 8, 623, 75, 91, 69, 65, 115, 707, 81, 53, 45, 41, 12, 103, 659, 57, 94, 29, 615, 611, 6, 93, 579, 33, 100, 50, 603, 695, 70, 689, 112, 97, 71, 507, 616, 719, 114, 109, 26, 711, 88, 647, 46, 641, 74, 117, 47, 441, 688

Offset: 0

Antti Karttunen, Aug 13 2016

Inverse: A275835.
Cf. A225901,  A255411, A257684, A273668.
Cf. also A275837, A275838.

(define (A275836 n) (A225901 (A273668 n)))

a(n) = A225901(A273668(n)).
Other identities. For all n >= 0:
a(n) = A257684(a(A255411(n))). [Restriction to A255411 induces the same permutation.]

A273667 Permutation of nonnegative integers: a(0) = 0, a(A153880(n)) = A255411(a(n)), a(A273670(n)) = A256450(a(n)).

Original entry on oeis.org

0, 1, 4, 2, 6, 3, 18, 8, 12, 5, 24, 10, 48, 15, 16, 7, 30, 13, 56, 20, 21, 9, 36, 17, 96, 67, 60, 26, 27, 11, 72, 42, 22, 23, 120, 81, 240, 73, 66, 32, 33, 14, 87, 49, 28, 29, 144, 101, 360, 270, 88, 89, 80, 38, 90, 39, 52, 19, 107, 57, 288, 34, 76, 35, 168, 125, 416, 303, 109, 110, 99, 44, 420, 111, 108, 45, 61, 25, 112, 131, 64, 68, 327, 40

Offset: 0

Antti Karttunen, May 30 2016

Antti Karttunen, Table of n, a(n) for n = 0..5039
Indranil Ghosh, Python program for computing this sequence
Index entries for sequences related to factorial base representation
Index entries for sequences that are permutations of the natural numbers

Inverse: A273668.
Cf. A153880, A225901, A255411, A256450, A257680, A266193, A273663, A273670.
Similar or related permutations: A255566, A273665.

a(0) = 0; for n >= 1: if A257680(A225901(n)) = 0 [when n is one of the terms of A153880] then a(n) = A255411(a(A266193(n))), otherwise [when n is one of the terms of A273670], a(n) = A256450(a(A273663(n))).
As a composition of other permutations:
a(n) = A255566(A273665(n)).

A275848 Permutation of natural numbers: a(0) = 0, a(A255411(n)) = A153880(a(n)), a(A256450(n)) = A273670(n).

Original entry on oeis.org

0, 1, 3, 4, 2, 5, 7, 9, 10, 11, 13, 15, 8, 16, 17, 18, 12, 19, 6, 20, 21, 22, 14, 23, 25, 27, 28, 29, 31, 33, 34, 35, 37, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 51, 52, 53, 55, 57, 26, 58, 59, 61, 32, 63, 64, 65, 66, 67, 68, 69, 36, 70, 71, 73, 38, 75, 50, 76, 77, 79, 56, 81, 30, 82, 83, 85, 60, 87, 88, 89, 90, 91, 92, 93, 62, 94, 95, 96, 72, 97, 48

Offset: 0

Antti Karttunen, Aug 13 2016

Inverse: A275847.
Cf. A153880, A255411, A256450, A257680, A257684, A273662, A273670.
Similar permutations: A273668 (a more recursed variant), A275845, A275846.

a(0) = 0; for n >= 1: if A257680(n) = 0 [when n is one of the terms of A255411] then a(n) = A153880(a(A257684(n))), otherwise [when n is one of the terms of A256450], a(n) = A273670(A273662(n)).

A255565 a(0) = 0; for n >= 1: if n = A255411(k) for some k, then a(n) = 2a(k), otherwise, n = A256450(h) for some h, and a(n) = 1 + 2a(h).

Original entry on oeis.org

0, 1, 3, 7, 2, 15, 5, 31, 11, 63, 23, 127, 6, 47, 255, 13, 14, 95, 4, 511, 27, 29, 30, 191, 9, 1023, 55, 59, 61, 383, 19, 2047, 111, 119, 123, 767, 39, 4095, 223, 239, 247, 1535, 79, 8191, 447, 479, 495, 3071, 10, 159, 16383, 895, 62, 959, 991, 6143, 21, 319, 32767, 1791, 22, 125, 1919, 1983, 126, 12287, 46, 43, 639, 65535, 254, 3583, 12

Offset: 0

Antti Karttunen, May 05 2015

Because all terms of A255411 are even it means that even terms can only occur in even positions (together with some odd terms, for each one of which there is a separate infinite cycle), while terms in odd positions are all odd.

Inverse: A255566.
Cf. A000079, A000142, A001511, A001563, A083318, A255411, A256450, A257679, A257680, A257682, A257685.
Cf. also arrays A257503, A257505.
Related or similar permutations: A273665, A273668.

a(0) = 0; for n >= 1: if A257680(n) = 0 [i.e., n is one of the terms of A255411], then a(n) = 2*a(A257685(n)), otherwise [when n is one of the terms of A256450], a(n) = 1 + 2*a(A273662(n)).
Other identities:
For all n >= 1, A001511(a(n)) = A257679(n).
For all n >= 1, a(A001563(n)) = A000079(n-1) = 2^(n-1).
For all n >= 1, a(A000142(n)) = A083318(n-1).

Formula changed because of the changed starting offset of A256450 - Antti Karttunen, May 30 2016

A273666 Permutation of nonnegative integers: a(0) = 0; after which, a(2n) = A153880(a(n)), a(2n+1) = A273670(a(n)).

Original entry on oeis.org

0, 1, 2, 3, 6, 4, 8, 5, 24, 10, 12, 7, 30, 13, 14, 9, 120, 34, 36, 16, 48, 18, 26, 11, 144, 42, 50, 19, 54, 20, 32, 15, 720, 154, 156, 46, 168, 49, 60, 22, 240, 66, 72, 25, 126, 37, 38, 17, 840, 186, 192, 58, 246, 68, 74, 27, 264, 73, 78, 28, 150, 44, 56, 21, 5040, 874, 876, 199, 888, 202, 204, 64, 960, 216, 242, 67, 288, 82, 84, 31

Offset: 0

Antti Karttunen, May 30 2016

This sequence can be represented as a binary tree. Each left hand child is produced as A153880(n), and each right hand child as A273670(n), when their parent contains n >= 1:
                                      0
                                      |
                   ...................1...................
                  2                                       3
        6......../ \........4                   8......../ \........5
       / \                 / \                 / \                 / \
      /   \               /   \               /   \               /   \
     /     \             /     \             /     \             /     \
   24       10         12       7          30       13         14       9
120  34   36  16     48  18   26 11     144  42   50  19     54  20   32 15
etc.

Inverse: A273665.
Cf. A153880, A273670.
Related or similar permutations: A255566, A273668.

a(0) = 0; after which, a(2n) = A153880(a(n)), a(2n+1) = A273670(a(n)).

A275846 Permutation of natural numbers: a(0) = 0, a(A255411(n)) = A153880(n), a(A256450(n)) = A273670(a(n)).

Original entry on oeis.org

0, 1, 3, 5, 2, 9, 4, 15, 7, 21, 11, 29, 6, 17, 41, 10, 8, 23, 12, 57, 16, 13, 14, 33, 18, 77, 22, 19, 20, 45, 25, 101, 31, 27, 28, 63, 35, 129, 43, 39, 40, 87, 47, 165, 59, 53, 55, 111, 24, 65, 213, 81, 26, 71, 75, 141, 34, 89, 269, 105, 30, 37, 95, 99, 32, 183, 36, 46, 113, 341, 38, 135, 48, 42, 51, 119, 50, 125, 44, 231, 49, 64, 143, 431, 54, 52

Offset: 0

Antti Karttunen, Aug 13 2016

Inverse: A275845.
Cf. A153880, A255411, A256450, A257680, A257684, A273662, A273670.
Similar permutations: A273668 (a more recursed variant), A275847, A275848.

a(0) = 0; for n >= 1: if A257680(n) = 0 [when n is one of the terms of A255411] then a(n) = A153880(A257684(n)), otherwise [when n is one of the terms of A256450], a(n) = A273670(a(A273662(n))).

A276958 Permutation of natural numbers: a(A255411(n)) = A153880(n), a(A256450(n)) = A273670(n).

Original entry on oeis.org

1, 3, 4, 2, 5, 7, 9, 10, 11, 13, 15, 6, 16, 17, 18, 8, 19, 12, 20, 21, 22, 14, 23, 25, 27, 28, 29, 31, 33, 34, 35, 37, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 51, 52, 53, 55, 57, 24, 58, 59, 61, 26, 63, 64, 65, 66, 67, 68, 69, 30, 70, 71, 73, 32, 75, 36, 76, 77, 79, 38, 81, 48, 82, 83, 85, 50, 87, 88, 89, 90, 91, 92, 93, 54

Offset: 1

Antti Karttunen, Sep 22 2016

Inverse: A276957.
Cf. A153880, A257680, A257684, A273670, A273662.
For more recursed variants see: A275846, A275848 & A273668.

(define (A276958 n) (cond ((zero? n) n) ((zero? (A257680 n)) (A153880 (A257684 n))) (else (A273670 (A273662 n)))))

If A257680(n) = 0, then a(n) = A153880(A257684(n)), otherwise a(n) = A273670(A273662(n)).

cp's OEIS Frontend

A275838 Permutation of nonnegative integers: a(n) = A273668(A225901(n)).

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A275836 Permutation of nonnegative integers: a(n) = A225901(A273668(n)).

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A273667 Permutation of nonnegative integers: a(0) = 0, a(A153880(n)) = A255411(a(n)), a(A273670(n)) = A256450(a(n)).

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A275848 Permutation of natural numbers: a(0) = 0, a(A255411(n)) = A153880(a(n)), a(A256450(n)) = A273670(n).

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A255565 a(0) = 0; for n >= 1: if n = A255411(k) for some k, then a(n) = 2*a(k), otherwise, n = A256450(h) for some h, and a(n) = 1 + 2*a(h).

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A273666 Permutation of nonnegative integers: a(0) = 0; after which, a(2n) = A153880(a(n)), a(2n+1) = A273670(a(n)).

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A275846 Permutation of natural numbers: a(0) = 0, a(A255411(n)) = A153880(n), a(A256450(n)) = A273670(a(n)).

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A276958 Permutation of natural numbers: a(A255411(n)) = A153880(n), a(A256450(n)) = A273670(n).

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Formula

A255565 a(0) = 0; for n >= 1: if n = A255411(k) for some k, then a(n) = 2a(k), otherwise, n = A256450(h) for some h, and a(n) = 1 + 2a(h).