A068016 Lonely non-twin primes: non-twins sandwiched between two pairs of twins.

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

Offset

1,1

Links

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.

Example

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.

Mathematica

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 *)

Crossrefs

Cf. A001097, A069453.

Sequence in context: A215163 A089685 A186883 * A338270 A140442 A078731

Adjacent sequences: A068013 A068014 A068015 * A068017 A068018 A068019

Keyword

nonn

Author

Neil Fernandez, Mar 22 2002

Extensions

More terms from Vladimir Joseph Stephan Orlovsky, Dec 04 2009

Status

approved