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%I #10 Oct 13 2017 11:23:43
%S 0,116,545,456,352,276,265,190,0,86,96,117,70,139,68,10,48,78,40,196,
%T 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,
%U 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
%N 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.
%C To get the total number of solutions including rotations and reflections, multiply a(n) by 8.
%e 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):
%e +----+----+----+
%e | 3 | 5 | 11 | --> 19
%e +----+----+----+
%e | 17 | 7 | 13 | --> 37
%e +----+----+----+
%e | 23 | 29 | 19 | --> 71
%e +----+----+----+
%e / vv vv vv \
%e 41 43 41 43 29
%Y Cf. A097232 (starting primes with no solutions), A097233 (starting primes with only one solution).
%K nonn
%O 1,2
%A Chuck Seggelin (seqfan(AT)plastereddragon.com), Jul 31 2004
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