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

1,2

Comments

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

Links

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

Example

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.

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 *)

Crossrefs

Cf. A000040, A005722, A006093, A127435.

Sequence in context: A023713 A032890 A092859 * A120424 A139440 A102607

Adjacent sequences: A173441 A173442 A173443 * A173445 A173446 A173447

Keyword

nonn

Author

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

Extensions

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

Definition clarified by Harvey P. Dale, Jun 24 2011

Status

approved