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.

2, 0, 3117, 504182416

Offset

1,1

Comments

a(n) > 0 for every n >= 3 under Dickson's conjecture.

References

Joseph S. Madachy, "Magic and Antimagic Squares." Ch. 4 in Madachy's Mathematical Recreations, New York: Dover, 1979, p. 95.

Clifford A. Pickover, The Mathematics of Oz: Mental Gymnastics from Beyond the Edge, Cambridge University Press, 2002, p. 327.

Links

Table of n, a(n) for n=1..4.

Wikipedia, Magic square

Wikipedia, Primes in arithmetic progression

Index entries for sequences related to magic squares

Example

      n = 3
|----|----|----|
|1669| 199|1249|
|----|----|----|
| 619|1039|1459|
|----|----|----|
| 829|1879| 409|
|----|----|----|
.
                  n = 4
|---------|---------|---------|---------|
| 53297929|189093589|179393899| 82396999|
|---------|---------|---------|---------|
|159994519|101796379|111496069|130895449|
|---------|---------|---------|---------|
|121195759|140595139|150294829| 92096689|
|---------|---------|---------|---------|
|169694209| 72697309| 62997619|198793279|
|---------|---------|---------|---------|

Crossrefs

Cf. A269324, A269905.

Sequence in context: A114632 A036108 A265594 * A090446 A270830 A270829

Adjacent sequences: A269901 A269902 A269903 * A269905 A269906 A269907

Keyword

nonn,hard,more

Author

Arkadiusz Wesolowski, Mar 07 2016

Status

approved