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 A064187 First of n^2 odd consecutive primes whose sum (=S) is divisible by n and S/n = n mod 2. 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A necessary condition for the existence of a magic square consisting of n^2 consecutive odd primes. LINKS EXAMPLE a(5)=13 since 13+17+ ... +113 = 1565 = 5*313 and 313 = 5 mod 2. 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, print(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

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Last modified January 23 22:26 EST 2019. Contains 319404 sequences. (Running on oeis4.)