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a(n) is the smallest m such that n!!-m and n!!+m are both primes.

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`%I #7 Sep 02 2017 11:01:19
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`%S 0,0,3,2,5,2,5,8,7,4,19,16,29,68,97,16,109,86,19,158,17,172,41,16,529,
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`%T 106,263,212,163,302,593,302,607,262,311,428,227,106,1271,8,229,386,
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`%U 1489,32,47,1996,1097,2566,41,632,1913,458,149,1244,2837,362,3317,908
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`%N a(n) is the smallest m such that n!!-m and n!!+m are both primes.
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`%C For n = 5,7,10,11,22,41,67,76,91,96,163,245,299,341, n!! is an interprime, the average of two consecutive primes, see A075275. See also n^n and n! as average of two primes in A075468 and A075409.
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`%e a(4) = 3 because 4!! = 8 and 8 -/+ 3 = 5 and 11 are primes with smallest equal distances from 4!!
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`%t smbp[n_]:=Module[{m=0,n2=n!!},While[Total[Boole[PrimeQ[n2+{m,-m}]]] != 2,m++];m]; Array[smbp,60,2] (* _Harvey P. Dale_, Sep 02 2017 *)
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`%Y Cf. A075275, A075468 and A075409.
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`%K nonn
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`%O 2,3
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`%A _Zak Seidov_, Sep 18 2002
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`%E More terms from _David Wasserman_, Jan 17 2005
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