A168079 Numbers n such that exactly one of n+-1, n+-2 and n+-3 is prime.

-1, 7, 11, 13, 17, 19, 24, 25, 27, 29, 31, 33, 35, 36, 41, 43, 48, 49, 51, 52, 54, 55, 57, 59, 61, 63, 65, 66, 71, 73, 75, 77, 78, 84, 85, 87, 88, 90, 91, 92, 94, 95, 96, 101, 103, 107, 109, 114, 115, 116, 124, 125, 126, 132, 133, 135, 137, 139, 141, 142, 146, 147, 149

Offset: 1

Author

Juri-Stepan Gerasimov, Nov 18 2009

Keywords

• sign

Examples

			a(1)=-1 (-4,-3,-2,0 and 1 are nonprimes, 2 is prime);
a(2)=7 (4,6,8,9 and 10 are nonprimes, 5 is prime);
a(3)=13 (8,9,10,12 and 14 are nonprimes, 11 is prime).
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A100317, A141468.

Programs

Mathematica

f[n_] := Length[Select[Drop[Range[n - 3, n + 3], {4}], PrimeQ]] == 1; Join[{-1}, Select[Range[0, 200], f]] (* G. C. Greubel, Jul 09 2016 *)
Join[{-1},Select[Range[200],Total[Boole[PrimeQ[Drop[Range[#-3,#+3],{4}]]]]==1&]] (* Harvey P. Dale, Oct 16 2018 *)

PARI

is(n)=isprime(n-3) + isprime(n-2) + isprime(n-1) + isprime(n+1) + isprime(n+2) + isprime(n+3) == 1 \\ Charles R Greathouse IV, Jun 13 2017

Formula

a(n) ~ 6n/log n. -Charles R Greathouse IV, May 25 2011

Extensions

Corrected (11, 57 inserted, 16 replaced by 126) by R. J. Mathar, Jun 04 2010