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a(n) = c is least number such that 10^n/2 -/+ c are primes.
2

%I #7 Dec 21 2014 12:21:17

%S 0,3,9,81,123,57,87,243,69,63,189,231,1569,381,231,1443,1113,321,339,

%T 1353,363,519,1323,1503,741,1221,957,1053,339,5931,2121,2301,2031,

%U 4773,4737,10281,1317,129,3873,1443,387,11769,8271,5337,2883,7137,8193,8493

%N a(n) = c is least number such that 10^n/2 -/+ c are primes.

%C Related to Goldbach pairs of 10^n: a(n)=10^n/2 -A124450(n) Lesser of pair of closest primes whose sum is 10^n. Cf. A124013 Lesser of pair of most widely separated primes whose sum is 10^n, A065577 Number of Goldbach partitions of 10^n

%C All terms are divisible by 3 - see A108163.

%e Next terms up to n = 101: 14637, 9897,

%e 6471, 183, 8043, 6921,6699, 29127, 3663, 12537, 3777,

%e 6741, 2253, 561, 3783, 26979, 16491, 6543, 10683,

%e 1749, 6417, 38871, 22767, 62403, 8631, 4497, 20739,

%e 453, 16731, 25293, 4341, 37467,

%e 55323,4587,37083,24717,6687,8763,22551,29367,37881,14301,8637,34101,22179,26811,7059,1647

%t lnc[n_]:=Module[{c=0,t=10^n/2},While[!AllTrue[t+{c,-c},PrimeQ],c++];c]; Array[ lnc,50] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Dec 21 2014 *)

%Y Cf. A065577, A124013, A124450.

%K nonn

%O 1,2

%A _Hans Havermann_ and _Zak Seidov_, Nov 03 2006