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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.

Showing 1-3 of 3 results.

A255554 Permutation of natural numbers: a(n) = A083221(A255552(n)).

Original entry on oeis.org

1, 2, 3, 4, 9, 6, 5, 8, 7, 10, 15, 12, 11, 14, 13, 16, 21, 18, 25, 20, 17, 22, 27, 24, 19, 26, 49, 28, 33, 30, 23, 32, 29, 34, 39, 36, 31, 38, 35, 40, 45, 42, 37, 44, 121, 46, 51, 48, 41, 50, 43, 52, 57, 54, 169, 56, 77, 58, 63, 60, 55, 62, 47, 64, 69, 66, 53, 68, 59, 70, 75, 72, 61, 74, 67, 76, 81, 78, 71, 80, 65, 82, 87, 84, 289, 86, 73, 88, 93, 90, 91, 92, 79
Offset: 1

Views

Author

Antti Karttunen, Feb 26 2015

Keywords

Comments

a(n) tells which number in array A083221, constructed from the sieve of Eratosthenes is at the same position where n is in array A255551 constructed from Lucky sieve. As both arrays have A005843 (even numbers) as their topmost row, this permutation fixes all of them.

Links

Crossrefs

Inverse: A255553.
Similar permutations: A255407, A255408, A249817, A249818.
Cf. A000040, A000959, A001248, A219178, A083141, A083221, A255550, A255552.

Programs

Formula

a(n) = A083221(A255552(n)).
Other identities:
a(2n) = 2n. [Fixes even numbers.]
For all n >= 1, a(A255550(n)) = A083141(n).
For all n >= 2, a(A000959(n)) = A000040(n).
For all n >= 2, a(A219178(n)) = A001248(n).

A255551 Lucky / Unlucky array, shifted version, read by antidiagonals A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...

Original entry on oeis.org

2, 4, 3, 6, 5, 7, 8, 11, 19, 9, 10, 17, 39, 27, 13, 12, 23, 61, 57, 45, 15, 14, 29, 81, 91, 97, 55, 21, 16, 35, 103, 121, 147, 117, 85, 25, 18, 41, 123, 153, 199, 181, 177, 109, 31, 20, 47, 145, 183, 253, 243, 277, 225, 139, 33, 22, 53, 165, 217, 301, 315, 369, 345, 295, 157, 37, 24, 59, 187, 247, 351, 379, 471, 465, 447, 325, 175, 43
Offset: 2

Views

Author

Antti Karttunen, Feb 26 2015

Keywords

Comments

Note how in comparison to A255545, the even numbers on the first row have been shifted one step left, "pushing" term 1 out of the array proper. This was done to obtain a better alignment with arrays like A083221 and A255127 associated with other sieves, from which one may then induce permutations like A255553 by cross-referencing.
The starting offset of the sequence giving the terms in square array is 2. However, we can tacitly assume that a(1) = 1 when the sequence is used one-dimensionally as a permutation of natural numbers.

Examples

			The top left corner of the array:
   2,   4,   6,   8,  10,  12,  14,   16,   18,   20,   22,   24,   26,   28,   30
   3,   5,  11,  17,  23,  29,  35,   41,   47,   53,   59,   65,   71,   77,   83
   7,  19,  39,  61,  81, 103, 123,  145,  165,  187,  207,  229,  249,  271,  291
   9,  27,  57,  91, 121, 153, 183,  217,  247,  279,  309,  343,  373,  405,  435
  13,  45,  97, 147, 199, 253, 301,  351,  403,  453,  507,  555,  609,  661,  709
  15,  55, 117, 181, 243, 315, 379,  441,  505,  571,  633,  697,  759,  825,  889
  21,  85, 177, 277, 369, 471, 567,  663,  757,  853,  949, 1045, 1141, 1239, 1333
  25, 109, 225, 345, 465, 589, 705,  829,  945, 1063, 1185, 1305, 1423, 1549, 1669
  31, 139, 295, 447, 603, 765, 913, 1075, 1227, 1377, 1537, 1689, 1843, 1999, 2155
  33, 157, 325, 493, 667, 835, 999, 1177, 1347, 1513, 1687, 1861, 2029, 2205, 2367
...

Links

Crossrefs

Inverse: A255552.
Variant of array A255545. (See also A255543).
Row 1: A005843 (even numbers).
Column 1: 2 followed by A000959(2..) (Lucky numbers from their second term onward).
Main diagonal: A255550.
Similar arrays: A083221, A255127.
Associated permutations: A255553, A255554.

Programs

Formula

For row = 1, A(row,col) = 2*col; For row > 1 and col = 1, A(row,col) = A000959(row); otherwise, A(row,col) = A255543(row,col-1).

A260435 Permutation mapping from Lucky sieve to Ludic sieve: a(1) = 1, for n > 1: a(n) = A255127(A260438(n), A260439(n)).

Original entry on oeis.org

1, 2, 3, 4, 9, 6, 5, 8, 7, 10, 15, 12, 11, 14, 13, 16, 21, 18, 19, 20, 17, 22, 27, 24, 23, 26, 31, 28, 33, 30, 25, 32, 29, 34, 39, 36, 37, 38, 35, 40, 45, 42, 41, 44, 55, 46, 51, 48, 43, 50, 47, 52, 57, 54, 73, 56, 59, 58, 63, 60, 49, 62, 53, 64, 69, 66, 61, 68, 67, 70, 75, 72, 71, 74, 77, 76, 81, 78, 83, 80, 65, 82, 87, 84, 101, 86, 89, 88
Offset: 1

Views

Author

Antti Karttunen, Jul 30 2015

Keywords

Comments

a(n) tells which number in array A255127 (constructed from Ludic sieve) is at the same position where n is in array A255551 (constructed from Lucky sieve). This permutation fixes all even numbers because both arrays have A005843 as their topmost row.

Links

Crossrefs

Inverse: A260436.
Cf. A000959, A003309, A255127, A260438, A260439.
Similar or related permutations: A255407, A255552, A255554, A249817, A249818, A260741 (a more recursed variant).

Programs

Formula

Other identities. For all n >= 1:
a(A000959(n+1)) = A003309(n+2). [Maps Lucky numbers to odd Ludic numbers.]
a(2n) = 2n.
As a composition of related permutations:
a(n) = A255127(A255552(n)).
a(n) = A255407(A255554(n)).
Showing 1-3 of 3 results.

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