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.

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

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..81.

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

Adjacent sequences: A097228 A097229 A097230 * A097232 A097233 A097234

Keyword

nonn

Author

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

Status

approved