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%I #9 Jan 13 2023 16:25:56
%S 137,55787,113131,179021,895789,1150649,3086003,4026103,4077559,
%T 8021753,8750857,12577063,14355559,19136527,19412863,20065961,
%U 21865339,22633141,25880177,30404971,33926159,38202173,41905891,42925699
%N Primes p = p(k) such that p(k) + p(k+11) = p(k+1) + p(k+10) = p(k+2) + p(k+9) = p(k+3) + p(k+8) = p(k+4) + p(k+7) = p(k+5) + p(k+6).
%F Primes p = prime(k) = A000040(k) such that A359440(k+5) >= 5. - _Peter Munn_, Jan 13 2023
%e 137 + 193 = 139 + 191 = 149 + 181 = 151 + 179 = 157 + 173 = 163 + 167.
%t a = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; Do[ a = Delete[ a, 1 ]; a = Append[ a, Prime[ n ] ]; If[ a[ [ 1 ] ] + a[ [ 12 ] ] == a[ [ 2 ] ] + a[ [ 11 ] ] == a[ [ 3 ] ] + a[ [ 10 ] ] == a[ [ 4 ] ] + a[ [ 9 ] ] == a[ [ 5 ] ] + a[ [ 8 ] ] == a[ [ 6 ] ] + a[ [ 7 ] ], Print[ a[ [ 1 ] ] ] ], {n, 1, 10^6} ]
%t okQ[n_]:=Length[Union[Take[n,6]+Reverse[Take[n,-6]]]]==1; Transpose[ Select[Partition[Prime[Range[2700000]],12,1],okQ]][[1]] (* _Harvey P. Dale_, Apr 25 2011 *)
%Y Cf. A000040, A022885, A064101, A359440.
%K easy,nonn
%O 1,1
%A _Robert G. Wilson v_, Sep 17 2001
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