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.

Showing 1-4 of 4 results.

A249741 Sieve of Eratosthenes minus one: a(n) = A083221(n+1) - 1.

Original entry on oeis.org

1, 3, 2, 5, 8, 4, 7, 14, 24, 6, 9, 20, 34, 48, 10, 11, 26, 54, 76, 120, 12, 13, 32, 64, 90, 142, 168, 16, 15, 38, 84, 118, 186, 220, 288, 18, 17, 44, 94, 132, 208, 246, 322, 360, 22, 19, 50, 114, 160, 252, 298, 390, 436, 528, 28, 21, 56, 124, 202, 318, 376, 492, 550, 666, 840, 30, 23, 62, 144, 216, 340, 402, 526, 588, 712, 898, 960, 36, 25
Offset: 1

Views

Author

Antti Karttunen, Nov 15 2014

Keywords

Examples

			The top left corner of the array:
   1,   3,   5,    7,    9,   11,   13,   15,   17,   19,   21,   23,   25,
   2,   8,  14,   20,   26,   32,   38,   44,   50,   56,   62,   68,   74,
   4,  24,  34,   54,   64,   84,   94,  114,  124,  144,  154,  174,  184,
   6,  48,  76,   90,  118,  132,  160,  202,  216,  258,  286,  300,  328,
  10, 120, 142,  186,  208,  252,  318,  340,  406,  450,  472,  516,  582,
  12, 168, 220,  246,  298,  376,  402,  480,  532,  558,  610,  688,  766,
  16, 288, 322,  390,  492,  526,  628,  696,  730,  798,  900, 1002, 1036,
  18, 360, 436,  550,  588,  702,  778,  816,  892, 1006, 1120, 1158, 1272,
  22, 528, 666,  712,  850,  942,  988, 1080, 1218, 1356, 1402, 1540, 1632,
  28, 840, 898, 1072, 1188, 1246, 1362, 1536, 1710, 1768, 1942, 2058, 2116,
...

Links

Crossrefs

Inverse: A249742.
Transpose: A114881.
Row 1: A005408, Column 1: A006093, Main diagonal: A249743.
Cf. also A002260, A004736, A038722, A083221.

Programs

Formula

a(n) = A083221(n+1) - 1.
As a composition of related permutations:
a(n) = A114881(A038722(n)).
a(n) = A249811(A135764(n)).

A249725 Inverse permutation to A135764.

Original entry on oeis.org

1, 3, 2, 6, 4, 5, 7, 10, 11, 8, 16, 9, 22, 12, 29, 15, 37, 17, 46, 13, 56, 23, 67, 14, 79, 30, 92, 18, 106, 38, 121, 21, 137, 47, 154, 24, 172, 57, 191, 19, 211, 68, 232, 31, 254, 80, 277, 20, 301, 93, 326, 39, 352, 107, 379, 25, 407, 122, 436, 48, 466, 138, 497, 28, 529, 155, 562, 58, 596, 173, 631, 32, 667, 192, 704, 69, 742, 212, 781, 26, 821, 233, 862, 81
Offset: 1

Views

Author

Antti Karttunen, Nov 15 2014

Keywords

Links

Crossrefs

Inverse: A135764.
Similar or related permutations: A209268, A246276, A246676, A249742, A249811.
Cf. A000079, A000124, A000217, A003602, A005408, A007814.

Programs

Formula

a(n) = 1 + (((A003602(n)+A007814(n))^2 + A007814(n) - A003602(n))/2).
As a composition of other permutations:
a(n) = A249742(A249811(n)).
a(n) = A246276(A246676(n)).
Other identities. For all n >= 0 the following holds:
a(A005408(n)) = A000124(n). [Maps odd numbers to central polygonal numbers].
a(A000079(n)) = A000217(n+1). [Maps powers of two to triangular numbers].

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).

A252460 Inverse permutation to A083221 considered as a permutation of natural numbers (with assumption that a(1) = 1).

Original entry on oeis.org

1, 2, 4, 3, 7, 5, 11, 8, 6, 12, 16, 17, 22, 23, 9, 30, 29, 38, 37, 47, 13, 57, 46, 68, 10, 80, 18, 93, 56, 107, 67, 122, 24, 138, 14, 155, 79, 173, 31, 192, 92, 212, 106, 233, 39, 255, 121, 278, 15, 302, 48, 327, 137, 353, 19, 380, 58, 408, 154, 437, 172, 467, 69, 498, 25, 530, 191, 563, 81, 597, 211, 632, 232, 668, 94, 705, 20
Offset: 1

Views

Author

Antti Karttunen, Dec 19 2014

Keywords

Links

Crossrefs

Essentially after a(1) one more than A249742.
Inverse permutation: A083221.
Cf. A055396, A078898.

Formula

a(1) = 1; for n>1: a(n) = 2 + ((((x+y)^2) - x - 3*y)/2), where x = A055396(n) and y = A078898(n).
a(1) = 1; for n>1: a(n) = 1 + A249742(n-1).
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.