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A269904 Smallest magic sum for any n X n magic square filled with primes in an arithmetic progression, or 0 if no such magic square exists.

%I A269904 #10 Mar 12 2016 22:23:00
%S A269904 2,0,3117,504182416
%N A269904 Smallest magic sum for any n X n magic square filled with primes in an arithmetic progression, or 0 if no such magic square exists.
%C A269904 a(n) > 0 for every n >= 3 under Dickson's conjecture.
%D A269904 Joseph S. Madachy, "Magic and Antimagic Squares." Ch. 4 in Madachy's Mathematical Recreations, New York: Dover, 1979, p. 95.
%D A269904 Clifford A. Pickover, The Mathematics of Oz: Mental Gymnastics from Beyond the Edge, Cambridge University Press, 2002, p. 327.
%H A269904 Wikipedia, <a href="http://en.wikipedia.org/wiki/Magic_square">Magic square</a>
%H A269904 Wikipedia, <a href="https://en.wikipedia.org/wiki/Primes_in_arithmetic_progression">Primes in arithmetic progression</a>
%H A269904 <a href="/index/Mag#magic">Index entries for sequences related to magic squares</a>
%e A269904       n = 3
%e A269904 |----|----|----|
%e A269904 |1669| 199|1249|
%e A269904 |----|----|----|
%e A269904 | 619|1039|1459|
%e A269904 |----|----|----|
%e A269904 | 829|1879| 409|
%e A269904 |----|----|----|
%e A269904 .
%e A269904                   n = 4
%e A269904 |---------|---------|---------|---------|
%e A269904 | 53297929|189093589|179393899| 82396999|
%e A269904 |---------|---------|---------|---------|
%e A269904 |159994519|101796379|111496069|130895449|
%e A269904 |---------|---------|---------|---------|
%e A269904 |121195759|140595139|150294829| 92096689|
%e A269904 |---------|---------|---------|---------|
%e A269904 |169694209| 72697309| 62997619|198793279|
%e A269904 |---------|---------|---------|---------|
%Y A269904 Cf. A269324, A269905.
%K A269904 nonn,hard,more
%O A269904 1,1
%A A269904 _Arkadiusz Wesolowski_, Mar 07 2016