A064013 Sum of first n^2 odd primes (=S) is divisible by n and S/n = n mod 2.

1, 35, 215, 225, 398, 2097, 5205, 7452, 22359, 98176, 169653

Offset

1,2

Comments

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

a(12) > 500000. - Donovan Johnson

Links

Table of n, a(n) for n=1..11.

Example

a(2)=35 since 3+5+ ... +9941 = 5706505 = 35*163043 and 163043 = 35 mod 2.

Prog

(PARI) s=0; t=0; u=1; forprime(x=3, 2500000, s=s+x; t=t+1; if(t==u*u, if(s%u==0&(s\u)%2==u%2, print(u), ); u=u+1, ))

Crossrefs

Sequence in context: A007329 A345655 A101628 * A240137 A020262 A224104

Adjacent sequences: A064010 A064011 A064012 * A064014 A064015 A064016

Keyword

nonn,hard

Author

H. K. Gottlob Maier (1korrago(AT)freenet.de), Sep 07, 2001

Extensions

a(10)-a(11) from Donovan Johnson, Nov 30 2010

Status

approved