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.

A118578 Numbers n such that A118799(n) = 0.

Original entry on oeis.org

21, 25, 29, 80, 1718, 4157, 4158, 5841, 20376, 23719, 28100, 28101, 28232, 32407, 32411, 45826, 49771, 56821, 58210, 59013, 62808, 63090, 63367, 65700, 66199, 71054, 82094, 83507, 86948, 94928, 95585, 99154, 101974, 126918, 126922, 127947
Offset: 1

Views

Author

Jonathan Vos Post, May 24 2006

Keywords

Examples

			a(1) = 21 because A118799(21) = 0 because of the singular matrix:
| 73  79  83  89|
| 97 101 103 107|
|109 113 127 131|
|137 139 149 151|.
a(4) = 80 because A118799(80) = 0 because of the singular matrix:
|409 419 421 431|
|433 439 443 449|
|457 461 463 467|
|479 487 491 499|.

Crossrefs

Cf. A000040, A118799.

Formula

n such that the following matrix is singular:
|prime(n) prime(n+1) prime(n+2) prime(n+3) |
|prime(n+4) prime(n+5) prime(n+6) prime(n+7) |
|prime(n+8) prime(n+9) prime(n+10) prime(n+11)|
|prime(n+12) prime(n+13) prime(n+14) prime(n+15)|

Extensions

More terms from Max Alekseyev, Sep 24 2011

A117330 a(n) is the determinant of the 3 X 3 matrix with entries the 9 consecutive primes starting with the n-th prime.

Original entry on oeis.org

-78, 20, -36, 36, -40, -96, 96, -480, -424, 520, 348, 100, -540, 144, -144, -712, 240, 96, 480, -1120, -468, -1152, -3384, 1404, -576, -3924, 7884, -1548, -7312, 6288, -1828, -528, -768, 1920, 720, 768, -1920, 2400, -944, -9340, 12588, 15540, -864, 5600, 4124, -13668, -1428, 1552
Offset: 1

Views

Author

Cino Hilliard and Walter Kehowski, Apr 24 2006

Keywords

Comments

The first term -78 is 6 mod 12 but all subsequent terms are 0,4,8 mod 12. Checked out to n=10000. A117329 is the subsequence formed by taking every 9th term.
The smallest absolute value of the sequence is 0.

Examples

			a(3)=-36 = det([[5,7,11],[13,17,19],[23,29,31]]).

Links

Crossrefs

Cf. A117329, A117345, A118799, A118815, A340869.

Programs

  • Maple
    primedet := proc(n) local L; L:=map(ithprime,[$n..n+8]); linalg[det]([L[1..3],L[4..6],L[7..9]]) end;
  • Mathematica
    Table[Det[Partition[Prime[Range[n,n+8]],3,3]],{n,50}] (* Harvey P. Dale, May 16 2019 *)
  • PARI
    a(n) = matdet(matrix(3,3,i,j,prime((n+j-1)+3*(i-1)))); \\ Michel Marcus, Jan 25 2021

Formula

a(A117345(n)) = 0. - Hugo Pfoertner, Jan 26 2021

Extensions

Edited by N. J. A. Sloane at the suggestion of Stefan Steinerberger, Jul 14 2007

A340924 8*a(n) is the maximum possible determinant of a 4 X 4 matrix whose entries are 16 consecutive primes starting with prime(n).

Original entry on oeis.org

608537, 837080, 1062261, 1335740, 1613011, 1834307, 2103606, 2369995, 2621808, 3072665, 3592140, 3891774, 4267302, 4412932, 4443915, 5039601, 5706864, 6673106, 7402050, 8535384, 9378963, 9989532, 10834096, 11530350, 11987568, 13560234, 14289963, 15119412, 15198123
Offset: 1

Views

Author

Hugo Pfoertner, Jan 26 2021

Keywords

Comments

The entries of the matrix are arranged in such a way that the determinant of the matrix is maximized.

Examples

			a(1) = 608537 = A180128(4)/8 with the corresponding matrix shown in A180128.
a(2) = 837080: determinant (
  [59 19 23  7]
  [11 53 37 13]
  [17  5 43 41]
  [29 31  3 47]) = 6696640 = 8*837080.

Crossrefs

Cf. A118799, A180128, A340923, A340925.

A118876 Determinant of n-th continuous block of 16 consecutive squares of primes.

Original entry on oeis.org

768280320, -1010949120, -4719098880, -1791590400, 24298444800, -19462947840, -109685145600, -3192514560, 144441833472, -198529367040, 15778022400, 159125783040, 861983659008, 1193361776640, 1359501373440, 5328357672960
Offset: 1

Views

Author

Jonathan Vos Post, May 24 2006

Keywords

Comments

Quadratic analog of A118799 Determinants of 4 X 4 matrices of continuous blocks of 16 consecutive primes. See also: A001248 Squares of primes. The terminology "continuous" is used to distinguish from "discrete" which would be block 1: 4, 9, 25, 49, 121, 169, 289, 361, 529, 841, 961, 1369, 1681, 1849, 2209, 2809; block 2: 3481, 3721, 4489, 5041, 5329, 6241, 6889, 7921, 9409, 10201, 10609, 11449, 11881, 12769, 16129, 17161; and so forth.

Examples

			a(1) = 768280320 =
|...4.....9...25....49.|
|.121...169..289...361.|
|.529...841..961..1369.|
|1681..1849.2209..2809.|.

Crossrefs

Cf. A000040, A001248, A117301, A117330, A118799.
Showing 1-4 of 4 results.

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

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