A176462 Numbers k such that neither k-1 nor k+1 is prime or semiprime.

0, 17, 19, 29, 31, 41, 43, 49, 51, 53, 55, 65, 67, 69, 71, 77, 79, 89, 91, 97, 99, 101, 103, 109, 111, 113, 115, 125, 127, 129, 131, 137, 139, 149, 151, 153, 155, 161, 163, 169, 171, 173, 175, 181, 183, 185, 187, 189, 191, 197, 199, 209, 211, 221, 223, 229, 231

Offset: 1

Author

Juri-Stepan Gerasimov, Apr 18 2010

Keywords

• nonn

Comments

a(n+1) is the (n+2)-th odd sum of two consecutive nonnegative nonprimes.

Examples

			0 is a term because neither 0-1=-1 nor 0+1=1 is prime or semiprime.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A141468.

Programs

Maple

isA001358 := proc(n) numtheory[bigomega](n) = 2 ; end proc: for n from 0 to 400 do if isA001358(n+1) or isA001358(n-1) or isprime(n+1) or isprime(n-1) then ; else printf("%d,",n) ; end if; end do: # R. J. Mathar, Apr 20 2010

Mathematica

Join[{0},Flatten[Position[Partition[Table[If[PrimeQ[n]||PrimeOmega[n] == 2,1,0],{n,250}],3,1],?(#[[1]]==#[[3]]==0&),{1},Heads -> False]]+ 1] (* _Harvey P. Dale, Oct 27 2015 *)

Formula

a(n+1) = A166685(n+2).

Extensions

Entries checked by R. J. Mathar, Apr 20 2010