A100317 Numbers k such that exactly one of k - 1 and k + 1 is prime.

1, 2, 3, 8, 10, 14, 16, 20, 22, 24, 28, 32, 36, 38, 40, 44, 46, 48, 52, 54, 58, 62, 66, 68, 70, 74, 78, 80, 82, 84, 88, 90, 96, 98, 100, 104, 106, 110, 112, 114, 126, 128, 130, 132, 136, 140, 148, 152, 156, 158, 162, 164, 166, 168, 172, 174, 178, 182, 190, 194, 196, 200

Offset: 1

Author

Rick L. Shepherd, Nov 13 2004

Keywords

• nonn

Comments

Beginning with a(2) = 3, n such that exactly one of n - 1 and n + 1 is composite.

Examples

			3 is in the sequence because 2 is prime but 4 is composite.
4 is not in the sequence because both 3 and 5 are prime.
5 is not in the sequence either because both 4 and 6 are composite.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A100318 (at least one of n - 1 and n + 1 is composite).

Cf. A001477, A169546, A171689, A099049, A014574 (no intersection with this sequence).

Programs

Magma

[n: n in [1..250] | IsPrime(n-1) xor IsPrime(n+1) ]; // G. C. Greubel, Apr 25 2019

Mathematica

Select[Range[250], Xor[PrimeQ[# - 1], PrimeQ[# + 1]] &] (* G. C. Greubel, Apr 25 2019 *)
Module[{nn=Table[If[PrimeQ[n],1,0],{n,0,220}],t1,t2},t1=Mean/@ SequencePosition[ nn,{1,,0}];t2=Mean/@SequencePosition[nn,{0,,1}];Flatten[ Join[t1,t2]]//Sort]-1 (* Harvey P. Dale, Jul 13 2019 *)

PARI

for(n=1,250,if(isprime(n-1)+isprime(n+1)==1,print1(n,",")))

Sage

[n for n in (1..250) if (is_prime(n-1) + is_prime(n+1) == 1)] # G. C. Greubel, Apr 25 2019