A174092 Primes p = -83 + n * 30 (n = 0, 1, ..., 8) forming "optimal" 3 x 3 Magic Prime Square.

-83, -53, -23, 7, 37, 67, 97, 127, 157

Offset

1,1

Comments

1st row: -53 157 7

2nd row: 97 37 -23

3rd row: 67 -83 127

Magic 3 x 3 square with minimal magic constant M = 3 * 37 = 111.

Elements are in arithmetic 1st-order progression, negative p are primes.

This magic prime square (MPS) from the author dates from 2008.

Note that Dudeney's MPS from 1917 has the nonprime element 1:

67 1 43

13 37 61

31 73 7

Madachy/Ondrejka gave 1979 MPS with M = 3 * 59 = 177 > 111:

17 89 71

113 59 5

47 29 101

References

E. Dudeney: Amusements in Mathematics, Problem 408, New York: Dover, 1970.

J. S. Madachy: Magic and Antimagic Squares, Madachy's Mathematical Recreations, New York, pp. 85-113, New York: Dover, 1979.

M. Miller: Geloeste und ungeloeste mathematische Probleme, Leipzig, 1982.

Links

Table of n, a(n) for n=1..9.

Crossrefs

Cf. A024351, A073519.

Sequence in context: A272637 A317915 A033403 * A346979 A134456 A247442

Adjacent sequences: A174089 A174090 A174091 * A174093 A174094 A174095

Keyword

base,fini,uned,sign

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Mar 07 2010

Status

approved