A179182 Natural numbers n such that n+1 or 2n+1 is prime.

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 23, 26, 28, 29, 30, 33, 35, 36, 39, 40, 41, 42, 44, 46, 48, 50, 51, 52, 53, 54, 56, 58, 60, 63, 65, 66, 68, 69, 70, 72, 74, 75, 78, 81, 82, 83, 86, 88, 89, 90, 95, 96, 98, 99, 100, 102, 105, 106, 108, 111, 112, 113, 114, 116, 119, 120, 125, 126, 128

Offset

1,2

Links

Table of n, a(n) for n=1..77.

Simon R. Blackburn, James F. McKee, Constructing k-radius sequences, Jun 30 2010.

Formula

{n: n such that n+1 is prime or 2*n+1 is prime} = {n: n such that n+1 is in A000040 or 2*n+1 is in A000040}.

Example

a(1) = 1 because 1+1 = 2 is prime.
a(2) = 2 because 2+1 = 3 is prime, or because 2*2+1 = 5 is prime.
a(3) = 3 because 2*3+1 = 7 is prime.
a(4) = 4 because 4+1 = 5 is prime.
a(5) = 5 because 2*5+1 = 11 is prime.
a(6) = 6 because 6+1 = 7 is prime, or because 2*6+1 = 13 is prime.
7 is not in the sequence because neither 7+1 = 8 nor 2*7+1 = 15 are prime.

Mathematica

fQ[n_] := PrimeQ[n + 1] || PrimeQ[2 n + 1]; Select[ Range@ 128, fQ@# &]
Select[Range[200], Or@@PrimeQ[{#+1, 2#+1}]&] (* Harvey P. Dale, Jun 11 2014 *)

Prog

(PARI) is(n)=isprime(n+1) || isprime(2*n+1) \\ Charles R Greathouse IV, Jun 13 2017

Crossrefs

Cf. A000040, A005097 (odd primes - 1)/2, A006093 (primes minus 1).

Sequence in context: A288712 A002180 A207333 * A298303 A333635 A364379

Adjacent sequences: A179179 A179180 A179181 * A179183 A179184 A179185

Keyword

easy,nonn

Author

Jonathan Vos Post, Jul 01 2010

Extensions

Corrected and extended the sequence and added the Mathematica coding Robert G. Wilson v, Jul 13 2010

Status

approved