

A097231


Number of solutions (excluding rotations and reflections) for a series of 9 consecutive primes beginning with the nth prime arranged in a 3 X 3 square such that all row, column and diagonal totals are primes.


3



0, 116, 545, 456, 352, 276, 265, 190, 0, 86, 96, 117, 70, 139, 68, 10, 48, 78, 40, 196, 15, 4, 0, 21, 7, 34, 20, 3, 21, 4, 9, 97, 55, 3, 26, 4, 0, 3, 28, 81, 85, 0, 19, 7, 3, 2, 0, 0, 0, 0, 0, 0, 3, 0, 23, 20, 2, 4, 5, 4, 0, 2, 7, 0, 11, 4, 0, 19, 0, 10, 0, 0, 0, 4, 9, 2, 7, 10, 11, 24, 1
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OFFSET

1,2


COMMENTS

To get the total number of solutions including rotations and reflections, multiply a(n) by 8.


LINKS



EXAMPLE

a(1) = 0 because there is no 3 X 3 square arrangement of the primes 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29 such that all row, column and diagonal totals are primes. a(2) = 116 because there are 116 unique 3 X 3 square arrangements of the primes 3, 5, 7, 11, 13, 17, 19, 23 and 29 such that all row, column and diagonal totals are primes. Here is one solution counted by a(2):
++++
 3  5  11  > 19
++++
 17  7  13  > 37
++++
 23  29  19  > 71
++++
/ vv vv vv \
41 43 41 43 29


CROSSREFS

Cf. A097232 (starting primes with no solutions), A097233 (starting primes with only one solution).


KEYWORD

nonn


AUTHOR

Chuck Seggelin (seqfan(AT)plastereddragon.com), Jul 31 2004


STATUS

approved



