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A068016
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Lonely non-twin primes: non-twins sandwiched between two pairs of twins.
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1
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23, 37, 67, 233, 277, 631, 1039, 1283, 1297, 1307, 1613, 1693, 1709, 2099, 2137, 2333, 2719, 2797, 3271, 3533, 3547, 3571, 3923, 4027, 4253, 4523, 4643, 4793, 5483, 5507, 5647, 6563, 7321, 8831, 8849, 9007, 9029, 10061, 10079, 10289, 10513, 12049, 13687
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OFFSET
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1,1
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LINKS
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Zak Seidov, Table of n, a(n) for n = 1..1000
Brian Hopkins, Euler's Enumerations, Enumerative Combinatorics and Applications (2021) Vol. 1, No. 1, Article #S1H1.
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EXAMPLE
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37 is in the sequence because it is adjacent to two pairs of twins (29,31 and 41,43). 47 is not because the primes adjacent to it are 43 and 53 and although 43 is a twin, 53 is not.
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MATHEMATICA
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PrimeNext[n_]:=Module[{k}, k=n+1; While[ !PrimeQ[k], k++ ]; k]; PrimePrev[n_]:=Module[{k}, k=n-1; While[ !PrimeQ[k], k-- ]; k]; lst={}; Do[p=Prime[n]; If[ !PrimeQ[p-2]&&PrimeQ[PrimePrev[p]-2]&&!PrimeQ[p+2]&&PrimeQ[PrimeNext[p]+2], AppendTo[lst, p]], {n, 7!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jul 22 2009 *)
m = 2000; #[[3]] & /@ Select[Partition[Prime[Range[7, m]], 5, 1], #[[2]] - #[[1]] == #[[5]] - #[[4]] == 2 &] (* Zak Seidov, Nov 25 2012 *)
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CROSSREFS
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Cf. A001097, A069453.
Sequence in context: A215163 A089685 A186883 * A338270 A140442 A078731
Adjacent sequences: A068013 A068014 A068015 * A068017 A068018 A068019
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KEYWORD
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nonn
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AUTHOR
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Neil Fernandez, Mar 22 2002
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EXTENSIONS
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More terms from Vladimir Joseph Stephan Orlovsky, Dec 04 2009
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STATUS
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approved
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