A100318 -id:A100318 - cp's OEIS frontend

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

Rick L. Shepherd, Nov 13 2004

nonn

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

			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.

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

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

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

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

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 *)

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

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

A100319 Even numbers m such that at least one of m-1 and m+1 is composite.

Original entry on oeis.org

8, 10, 14, 16, 20, 22, 24, 26, 28, 32, 34, 36, 38, 40, 44, 46, 48, 50, 52, 54, 56, 58, 62, 64, 66, 68, 70, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 104, 106, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 140, 142, 144, 146, 148

Offset: 1

Rick L. Shepherd, Nov 13 2004

nonn

Subsequence of A100318. For each k >= 0, a(k+1) = a(k) + 2 unless a(k) + 1 and a(k) + 3 are twin primes, in which case a(k+1) = a(k) + 4 (as a(k) - 1 and a(k) + 5 are divisible by 3).

The even nonisolated primes(n+1). - Juri-Stepan Gerasimov, Nov 09 2009

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

Cf. A100318 (supersequence containing odd and even n), A045718 (n such that at least one of n-1 and n+1 is prime).
Cf. A167692(the even nonisolated nonprimes). - Juri-Stepan Gerasimov, Nov 09 2009
Cf. A005818, A038179, A007310, A038511, A025584.
Complement of A014574 (average of twin prime pairs) w.r.t. A005843 (even numbers), except for missing term 2.

Select[2*Range[100], CompositeQ[#-1] || CompositeQ[#+1] &]  (* G. C. Greubel, Mar 09 2019 *)

forstep(n=4,300,2,if(isprime(n-1)+isprime(n+1)<=1,print1(n,",")))

[n for n in (3..250) if mod(n,2)==0 and (is_prime(n-1) + is_prime(n+1)) < 2] # G. C. Greubel, Mar 09 2019

a(n) = A167692(n+1). - Juri-Stepan Gerasimov, Nov 09 2009

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Sage