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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,1

COMMENTS

Classic pan-diagonal magic squares exist for orders n>3 not of the form 4k+2.

Non-traditional pan-diagonal 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

Table of n, a(n) for n=4..7.

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

Cf. A073523

Sequence in context: A099833 A272950 A255266 * A154378 A300145 A063372

Adjacent sequences:  A179437 A179438 A179439 * A179441 A179442 A179443

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

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Last modified October 14 05:04 EDT 2019. Contains 327995 sequences. (Running on oeis4.)