A173444 Either (n-th prime-1)^2-+1, but not both, is prime.

1, 3, 4, 5, 7, 12, 13, 19, 31, 32, 36, 37, 42, 47, 53, 54, 55, 58, 60, 63, 78, 79, 82, 83, 91, 94, 102, 105, 106, 118, 125, 126, 133, 135, 144, 155, 156, 159, 161, 163, 178, 184, 190, 206, 210, 214, 216, 219, 247, 248, 284, 286, 288, 307, 313, 315, 322, 336, 340, 344

Offset: 1

Author

Juri-Stepan Gerasimov, Feb 18 2010, Mar 27 2010

Keywords

• nonn

Comments

Numbers n such that either A005722(n)-+1 is prime.

Examples

			1 is in the sequence because (1st prime-1)^2-1=0 is nonprime and (1st prime-1)^2+1=2 is prime;
3 is in the sequence because (3rd prime-1)^2-1=15 is nonprime and (3rd prime-1)^2+1=17 is prime.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A005722, A006093, A127435.

Programs

Maple

A005722 := proc(n) (ithprime(n)-1)^2 ; end proc: for n from 1 to 800 do a := A005722(n) ; if isprime(a-1) <> isprime(a+1) then printf("%d,",n) ; end if; end do: # R. J. Mathar, Apr 24 2010

Mathematica

ppQ[n_]:=Module[{c=(Prime[n]-1)^2},Sort[PrimeQ[{c+1,c-1}]]== {False, True}]; Select[Range[400],ppQ] (* Harvey P. Dale, Jun 24 2011 *)
Select[Range[400],Total[Boole[PrimeQ[(Prime[#]-1)^2+{1,-1}]]]==1&] (* Harvey P. Dale, Feb 01 2023 *)

Extensions

More terms from R. J. Mathar, Apr 24 2010

Definition clarified by Harvey P. Dale, Jun 24 2011