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A179440
The smallest magic constant of pan-diagonal magic squares which consist of distinct prime numbers
1
240, 395, 450, 733
OFFSET
4,1
COMMENTS
Classic pan-diagonal magic squares exist for orders n > 3 not of the form 4k+2.
Non-traditional pandiagonal magic squares exist for all orders n > 3.
Bounds for further terms: a(8) <= 1248, a(9) <= 2025, a(10) <= 2850, a(11) <= 4195, a(12) <= 5544, a(13) <= 7597.
LINKS
N. Makarova, (in Russian)
V. Pavlovsky, (in Russian)
S. Belyaev , (in Russian)
Mutsumi Suzuki, MagicSquare
Al Zimmermann's Programming Contests, Pandiagonal Magic Squares of Prime Numbers: Final Report
EXAMPLE
a(5) = 395 (found by V. Pavlovsky)
5 73 127 137 53
37 167 17 71 103
83 101 13 67 131
43 31 197 113 11
227 23 41 7 97
.
a(6) = 450 (found by Radko Nachev)
3 5 89 137 67 149
127 163 7 29 11 113
31 23 167 59 157 13
107 97 43 53 131 19
73 79 41 71 47 139
109 83 103 101 37 17
.
a(7) = 733 (found by Jarek Wroblewski)
3 7 173 223 17 197 113
181 211 11 79 131 23 97
43 41 149 89 137 191 83
233 103 107 73 127 31 59
29 167 101 19 199 67 151
5 47 139 179 109 61 193
239 157 53 71 13 163 37
CROSSREFS
Sequence in context: A099833 A272950 A255266 * A154378 A300145 A063372
KEYWORD
more,nonn,bref
AUTHOR
Natalia Makarova, Jul 14 2010
EXTENSIONS
Correction for the third term with example given Natalia Makarova, Jul 21 2010
Link and example corrected by Natalia Makarova, Aug 01 2010
Edited by Max Alekseyev, Mar 15 2011
Bound for a(9) improved by Alex Chernov, Apr 23 2011
Bound for a(12) improved by _Natalya Makarova_, Jun 21 2011
Corrected a(6) from Radko Nachev, added by Max Alekseyev, May 28 2013
a(7) from Jarek Wroblewski and new bounds from Al Zimmermann's contest, added by Max Alekseyev, Oct 11 2013
STATUS
approved