cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A246273 Transpose of square array A246275.

Original entry on oeis.org

1, 2, 3, 4, 8, 5, 6, 24, 14, 7, 10, 48, 34, 26, 9, 12, 120, 76, 124, 20, 11, 16, 168, 142, 342, 54, 44, 13, 18, 288, 220, 1330, 90, 174, 32, 15, 22, 360, 322, 2196, 186, 538, 64, 80, 17, 28, 528, 436, 4912, 246, 1572, 118, 624, 74, 19, 30, 840, 666, 6858, 390, 2872, 208, 2400, 244, 62, 21
Offset: 1

Views

Author

Antti Karttunen, Aug 21 2014

Keywords

Examples

			The top-left corner of the array:
   1,     2,     4,     6,    10,    12,    16,    18,    22,   ...
   3,     8,    24,    48,   120,   168,   288,   360,   528,   ...
   5,    14,    34,    76,   142,   220,   322,   436,   666,   ...
   7,    26,   124,   342,  1330,  2196,  4912,  6858, 12166,   ...
   9,    20,    54,    90,   186,   246,   390,   550,   712,   ...
  11,    44,   174,   538,  1572,  2872,  5490,  8302, 15340,   ...
  ...

Links

Crossrefs

Inverse permutation: A246274.
Transpose: A246275.
Other related permutations: A038722, A054582, A246675, A246676.
One less than A246279.
Cf. A114881.

Programs

Formula

a(n) = A246279(n) - 1.
As a composition of related permutations:
a(n) = A246275(A038722(n)).
a(n) = A246676(A054582(n-1)).

A246677 Permutation of natural numbers: a(1) = 1, a(2n) = A000079(A055396(2n+1)-1) * ((2*A246277(2n+1))-1), a(2n+1) = 1 + 2*a(n).

Original entry on oeis.org

1, 2, 3, 4, 5, 8, 7, 6, 9, 16, 11, 32, 17, 10, 15, 64, 13, 128, 19, 18, 33, 256, 23, 12, 65, 14, 35, 512, 21, 1024, 31, 26, 129, 20, 27, 2048, 257, 42, 39, 4096, 37, 8192, 67, 22, 513, 16384, 47, 24, 25, 50, 131, 32768, 29, 36, 71, 66, 1025, 65536, 43, 131072, 2049, 38, 63, 52, 53, 262144, 259, 74, 41
Offset: 1

Views

Author

Antti Karttunen, Sep 01 2014

Keywords

Comments

See the comments in A246675. This is otherwise similar permutation, except for odd numbers, which are here recursively permuted by the emerging permutation itself. The even bisection halved gives A246679, the odd bisection from a(3) onward with one subtracted and then halved gives this sequence back.

Links

Crossrefs

Inverse: A246678. Variants: A246675, A246683.
Even bisection halved: A246679.
Cf. A000079, A055396, A246277.
a(n) differs from A156552(n+1) for the first time at n=32, where a(32) = 26, while A156552(33) = 34.

Formula

a(1) = 1, a(2n) = A000079(A055396(2n+1)-1) * ((2*A246277(2n+1))-1), a(2n+1) = 1 + 2*a(n).

A249812 Permutation of natural numbers: a(n) = A000079(A055396(n+1)-1) * ((2*A078898(n+1))-1).

Original entry on oeis.org

1, 2, 3, 4, 5, 8, 7, 6, 9, 16, 11, 32, 13, 10, 15, 64, 17, 128, 19, 14, 21, 256, 23, 12, 25, 18, 27, 512, 29, 1024, 31, 22, 33, 20, 35, 2048, 37, 26, 39, 4096, 41, 8192, 43, 30, 45, 16384, 47, 24, 49, 34, 51, 32768, 53, 28, 55, 38, 57, 65536, 59, 131072, 61, 42, 63, 36, 65, 262144, 67, 46, 69, 524288, 71, 1048576, 73, 50, 75, 40, 77, 2097152, 79, 54, 81, 4194304, 83, 44
Offset: 1

Views

Author

Antti Karttunen, Nov 06 2014

Keywords

Comments

In the essence, a(n) tells which number in the array A135764 is at the same position where n is in the array A249741, the sieve of Eratosthenes minus 1. As the topmost row in both arrays is A005408 (odd numbers), they are fixed, i.e., a(2n+1) = 2n+1 for all n.
Equally: a(n) tells which number in array A054582 is at the same position where n is in the array A114881, as they are the transposes of above two arrays.

Links

Crossrefs

Inverse: A249811.
Cf. A000079, A005408, A006093, A055396, A078898.
Similar or related permutations: A249813 ("deep variant"), A246675, A249816, A054582, A114881, A250252, A135764, A249741, A249742.
Differs from A246675 for the first time at n=20, where a(20)=14, while A246675(20)=18.

Programs

Formula

a(n) = A000079(A055396(n+1)-1) * ((2*A078898(n+1))-1).
As a composition of related permutations:
a(n) = A054582(A250252(n)-1).
a(n) = A135764(A249742(n)).
a(n) = A246675(A249816(n)).
Other identities. For all n >= 1 the following holds:
a(A006093(n)) = A000079(n-1).

A246274 Inverse of A246273 considered as a permutation of natural numbers.

Original entry on oeis.org

1, 2, 3, 4, 6, 7, 10, 5, 15, 11, 21, 16, 28, 9, 36, 22, 45, 29, 55, 20, 66, 37, 78, 8, 91, 14, 105, 46, 120, 56, 136, 35, 153, 13, 171, 67, 190, 77, 210, 79, 231, 92, 253, 27, 276, 106, 300, 12, 325, 104, 351, 121, 378, 26, 406, 170, 435, 137, 465, 154, 496, 65, 528, 43, 561, 172, 595, 209, 630, 191, 666, 211, 703, 54, 741, 18
Offset: 1

Views

Author

Antti Karttunen, Aug 21 2014

Keywords

Links

Crossrefs

Inverse: A246273.
Related permutations: A209268, A246675, A246276.
Cf. A055396, A246277.

Programs

  • Scheme
    (define (A246274 n) (let ((x (A246277 (+ 1 n))) (y (A055396 (+ 1 n)))) (* (/ 1 2) (- (expt (+ x y) 2) x y y y -2))))

Formula

a(n) = ((x+y)^2 - x - 3y + 2)/2, where x = A246277(n+1) and y = A055396(n+1).
As a composition of related permutations:
a(n) = A209268(A246675(n)).
Previous Showing 11-14 of 14 results.

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