A202298 If A is the n X n matrix containing the first n^2 primes, a(n) is the sum of the elements of the square of A.

4, 155, 3702, 39933, 244676, 1046455, 3635046, 10406049, 26595892, 60712839, 128248632, 253217949, 472633812, 837636667, 1431878468, 2356057659, 3756191658, 5844567389, 8865989698, 13147819241, 19100995732, 27324708263, 38402817766, 53116446341, 72537301810, 97894517685

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Formula

a(n) = Sum_{j=1..n} (Sum_{i=1..n} prime(i+n*(j-1)) * Sum_{i=1..n} prime(j+n*(i-1))). - Robert Israel, Jan 11 2024

Example

M2 = [2,3; 5,7], M2*M2 = [19,27; 45,64], so a(2) = 19 + 27 + 45 + 64 = 155.

Maple

A202298 := proc(n)
    local A, A2, r, c ;
    A := Matrix(n, n) ;
    for r from 0 to n-1 do
    for c from 0 to n-1 do
        A[r+1, c+1] := ithprime(1+r*n+c) ;
    end do:
    end do:
    A2 := A^2 ;
    add(add(A2[r, c], r=1..n), c=1..n) ;
end proc: # R. J. Mathar, Feb 09 2017
# alternative
N:= 50: # for a(1)..a(N)
P:= [seq(ithprime(i), i=1..N^2)]:
f:= proc(n) local M, e, u; M:= Matrix(n, n, P[1..n^2]);
   e:= Vector(n, 1);
   e^%T . (M . (M . e));
end proc:
map(f, [$1..N]); # Robert Israel, Jan 11 2024

Prog

(PARI) a(n) = my(m = matrix(n, n, i, j, prime((i-1)*n+j))); my(mm = m^2); sum(k=1, n, vecsum(mm[k, ])); \\ Michel Marcus, Jan 28 2017

Crossrefs

Cf. A000040, A109724.

Sequence in context: A303898 A370230 A093977 * A003736 A354285 A210837

Adjacent sequences: A202295 A202296 A202297 * A202299 A202300 A202301

Keyword

nonn

Author

Stephen Balaban, Dec 15 2011

Extensions

More terms from Michel Marcus, Jan 28 2017

Status

approved