A350200 - OEIS

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A350200

Array read by antidiagonals: T(n,k) is the determinant of the Hankel matrix of the 2*n-1 consecutive primes starting at the k-th prime, n >= 0, k >= 1.

1, 1, 2, 1, 3, 1, 1, 5, -4, -2, 1, 7, 6, 12, 0, 1, 11, -30, -72, 144, 288, 1, 13, 18, 72, 0, 576, -1728, 1, 17, -42, -72, 288, 1152, -7104, -26240, 1, 19, 30, -96, 144, -1248, -11712, 45248, 222272, 1, 23, 22, -188, 488, -112, -11360, 21184, 450432, 1636864

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Table of n, a(n) for n=0..54.

Wikipedia, Hankel matrix

EXAMPLE

Array begins:

n\k| 1 2 3 4 5 6 7 8

---+--------------------------------------------------------------

0 | 1 1 1 1 1 1 1 1

1 | 2 3 5 7 11 13 17 19

2 | 1 -4 6 -30 18 -42 30 22

3 | -2 12 -72 72 -72 -96 -188 -480

4 | 0 144 0 288 144 488 1800 2280

5 | 288 576 1152 -1248 -112 4432 -1552 15952

6 | -1728 -7104 -11712 -11360 -10816 29952 -89152 -57088

7 | -26240 45248 21184 -103168 -43264 -605440 -379264 271552

8 | 222272 450432 1068800 2022912 3927552 5399552 6315904 6861312

T(3,2) = 12, the determinant of the Hankel matrix

[3 5 7]

[5 7 11]

[7 11 13].

PROG

(Python)

from sympy import Matrix, prime, nextprime

def A350200(n, k):

p = [prime(k)] if n > 0 else []

for i in range(2*n-2): p.append(nextprime(p[-1]))

return Matrix(n, n, lambda i, j:p[i+j]).det()

CROSSREFS

Cf. A350201.

Cf. A000012 (row n = 0), A000040 (row n = 1), A056221 (row n = 2 with opposite sign), A024356 (column k = 1), A071543 (column k = 2).

Sequence in context: A110619 A354234 A191861 * A129761 A319299 A207031

Adjacent sequences: A350197 A350198 A350199 * A350201 A350202 A350203

KEYWORD

sign,tabl

AUTHOR

Pontus von Brömssen, Dec 19 2021

EXTENSIONS

Offset corrected by Pontus von Brömssen, Aug 25 2022

STATUS

approved