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

0,2

Links

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

Formula

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

Mathematica

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

Prog

(Clojure) (defn prod-prime-matrix [n] (* (sum-matrix (first-n2-primes n)) (sum-matrix (first-n2-primes (inc n)))))
(Magma) A109724:=func<n|&+[NthPrime(h): h in [1..n^2]]>; [0] cat [A109724(n)*A109724(n+1): n in [1..23]];  // Bruno Berselli, Dec 16 2011
(PARI) a(n) = vecsum(primes(n^2))* vecsum(primes((n+1)^2)); \\ Michel Marcus, Mar 20 2023

Crossrefs

Cf. A109724.

Sequence in context: A123790 A297636 A212033 * A296673 A086881 A212023

Adjacent sequences: A202294 A202295 A202296 * A202298 A202299 A202300

Keyword

nonn

Author

Stephen Balaban, Dec 15 2011

Extensions

More terms from Bruno Berselli, Dec 16 2011

Status

approved