Stephen Balaban - cp's OEIS frontend

User: Stephen Balaban

Stephen Balaban has authored 2 sequences.

A202297 Product of the sum of the first n^2 primes by the sum of the first (n+1)^2 primes.

0, 34, 1700, 38100, 403860, 2572620, 11863176, 43468984, 134426588, 364794428, 890218104, 1998186072, 4178379984, 8232956688, 15425693558, 27713583130, 47890427740, 80095432340, 130221623840, 206201325600, 318555575550, 481995772662, 715882366878, 1043383039482

Offset: 0

Stephen Balaban, Dec 15 2011

nonn

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Stephen Balaban, Clojure Code for generating the sequence usage: clj primes.txt n where n is the number of elements of this sequence to print

Cf. A109724.

(defn prod-prime-matrix [n] (* (sum-matrix (first-n2-primes n)) (sum-matrix (first-n2-primes (inc n)))))

A109724:=func; [0] cat [A109724(n)*A109724(n+1): n in [1..23]];  // Bruno Berselli, Dec 16 2011

Table[(Plus@@Prime[Range[n^2]]) (Plus@@Prime[Range[(n + 1)^2]]), {n, 0, 19}] (* Alonso del Arte, Dec 16 2011 *)

a(n) = vecsum(primes(n^2))* vecsum(primes((n+1)^2)); \\ Michel Marcus, Mar 20 2023

a(n) = A109724(n)*A109724(n+1).

More terms from Bruno Berselli, Dec 16 2011

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.

Original entry on oeis.org

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

Stephen Balaban, Dec 15 2011

nonn

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

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

Cf. A000040, A109724.

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

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

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

More terms from Michel Marcus, Jan 28 2017

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User: Stephen Balaban

A202297 Product of the sum of the first n^2 primes by the sum of the first (n+1)^2 primes.

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