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A097231 Number of solutions (excluding rotations and reflections) for a series of 9 consecutive primes beginning with the n-th 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 (list; graph; refs; listen; history; text; internal format)
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).
Sequence in context: A259584 A184069 A096925 * A203251 A238924 A076044
KEYWORD
nonn
AUTHOR
Chuck Seggelin (seqfan(AT)plastereddragon.com), Jul 31 2004
STATUS
approved

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Last modified July 23 23:47 EDT 2024. Contains 374575 sequences. (Running on oeis4.)