A073350 Primes not at the center of a 3 X 3 magic square of primes.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 61, 67, 79, 83, 97, 101, 107, 113, 163, 181, 197, 199, 223, 229, 233, 277, 313, 317, 331, 433, 439, 457, 569, 859

Offset: 1

Author

David W. Wilson, Aug 25 2002

Keywords

• nonn

Comments

The "magic sum" is always thrice the central entry.

There are no other terms < 5000.

There are no other terms < 100000. - Robert Israel, Feb 16 2016

Links

• Index entries for sequences related to magic squares

Crossrefs

Cf. A073473. A magic square with 59 at center is given in A024351.

Programs

Maple

N:= 10000: # to get all terms <= N
P:= select(isprime,{seq(p,p=3..2*N,2)}):
count:= 1:
A[count]:= 2:
for ic from 1 while P[ic] <= N do
   c:= P[ic];
   V:= map(`-`,P[ic+1..-1],c) intersect map(t -> c-t, P[1..ic-1]);
   nv:= nops(V);
   VV:= {seq(seq(V[j]-V[i],j=i+1..nv),i=1..nv-1)} intersect V;
   nvv:= nops(VV);
   found:= false;
   for ia from 1 to nvv while not found do
     a:= VV[ia];
     for ib from ia+1 to nvv while VV[ib] < c - a do
       b:= VV[ib];
       if b <> 2*a and {c-a-b,c-a+b,c-b+a,c+a+b} subset P then
          found:= true;
          break
       fi
     od
   od:
   if not found then
     count:= count+1;
     A[count]:= c;
   fi
od:
seq(A[i],i=1..count); # Robert Israel, Feb 16 2016