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A118799 Determinants of 4 X 4 matrices of continuous blocks of 16 consecutive primes. 3
880, -448, -1472, -240, 2480, -1352, -4128, -96, 2736, -2520, 120, 1080, 4288, 4880, 4600, 13368, 7056, 14560, 2960, 13320, 0, 24864, -11096, -24264, 0, -9168, -2128, -15792, 0, 18120, -5248, 6384, -21840, -38776, -20480, 20176, -72896, -69200, 40080, -37632 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

4 X 4 analog of A117330 Determinants of 3 X 3 matrices of continuous blocks of 9 consecutive primes. The terminology "continuous" is used to distinguish from "discrete" which would be (in this 4 X 4 prime case) block 1: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53; block 2: 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131; and so forth.

All terms are even. - Harvey P. Dale, May 05 2016

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

EXAMPLE

a(1) = 880 because the determinant of the first continuous block of 16 primes is:

| 2. 3. 5. 7.|

|11. 13. 17. 19.|

|23. 29. 31. 37.|

|41. 43. 47. 53.|.

a(10) = -2520 because the determinant of the 10th continuous block of 16 primes is:

|29. 31. 37. 41.|

|43. 47. 53. 59.|

|61. 67. 71. 73.|

|79. 83. 89. 97.|.

a(21) = 0 because of the singular matrix:

| 73. 79. 83. 89.|

| 97. 101. 103. 107.|

|109. 113. 127. 131.|

|137. 139. 149. 151.|.

a(25) = 0 because of the singular matrix:

| 97. 101. 103. 107.|

|109. 113. 127. 131.|

|137. 139. 149. 151.|

|157. 163. 167. 173.|

MAPLE

A118799 := proc(n)

    local A, i, r, c ;

    A := Matrix(4, 4) ;

    i := n ;

    for r from 1 to 4 do

    for c from 1 to 4 do

        A[r, c] := ithprime(i) ;

        i := i+1 ;

    end do:

    end do:

    LinearAlgebra[Determinant](A) ;

end proc: # R. J. Mathar, May 05 2013

MATHEMATICA

Module[{nn=60, prs}, prs=Prime[Range[nn]]; Table[Det[Partition[ Take[ prs, {n, n+15}], 4]], {n, nn-15}]] (* Harvey P. Dale, Apr 29 2016 *)

CROSSREFS

Cf. A000040, A067276, A117301, A118713.

Sequence in context: A129313 A063051 A190030 * A206341 A024393 A006052

Adjacent sequences:  A118796 A118797 A118798 * A118800 A118801 A118802

KEYWORD

easy,sign

AUTHOR

Jonathan Vos Post, May 23 2006

STATUS

approved

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Last modified May 29 16:53 EDT 2017. Contains 287252 sequences.