A064187 First of n^2 consecutive odd primes whose sum (=S) is divisible by n and S/n == n (mod 2).

3, 5, 23, 5, 13, 7, 7, 79, 37, 23, 67, 89, 13, 89, 131, 31, 71, 47, 43, 73, 277, 353, 41, 67, 127, 223, 79, 13, 193, 5, 23, 43, 5, 67, 3, 19, 5, 59, 59, 653, 19, 19, 97, 409, 5, 383, 29, 137, 379, 349, 653, 1187, 47, 41, 37, 17, 619, 89, 283, 283, 43, 479, 191

Offset

1,1

Comments

A necessary condition for the existence of a magic square consisting of n^2 consecutive odd primes.

Links

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

Example

a(5)=13 since 13+17+ ... +113 = 1565 = 5*313 and 313 == 5 (mod 2).

Maple

P:= select(isprime, [seq(i, i=3..10^6, 2)]):
nP:= nops(P):
PS:= [0, op(ListTools:-PartialSums(P))]:
f:= proc(n) local i, s;
  for i from 1 to nP+1-n^2 do
    s:= PS[i+n^2]-PS[i];
    if s mod n = 0 and (s/n - n) mod 2= 0 then return P[i] fi
  od;
  FAIL
end proc;
map(f, [$1..100]); # Robert Israel, Jul 18 2023

Prog

(PARI) for(n=1, 50, k=2; m=n^2; aflag=0; while(k+m<=500000&&aflag==0, s=0; for(x=k, k+m-1, s=s+prime(x)); if(s%n==0&&(s/n)%2==n%2, print1(prime(k), ", "); aflag=1); k++))

Crossrefs

Position of 3's gives A064013.

Sequence in context: A178377 A270621 A270637 * A112686 A318443 A272426

Adjacent sequences: A064184 A064185 A064186 * A064188 A064189 A064190

Keyword

nonn

Author

H. K. Gottlob Maier (1korrago(AT)freenet.de), Sep 20 2001

Status

approved