A104278 Numbers m such that 2m+1 and 2m-1 are not primes.

13, 17, 25, 28, 32, 38, 43, 46, 47, 58, 59, 60, 61, 62, 67, 71, 72, 73, 77, 80, 85, 88, 92, 93, 94, 101, 102, 103, 104, 107, 108, 109, 110, 118, 122, 123, 124, 127, 130, 133, 137, 143, 144, 145, 148, 149, 150, 151, 152, 160, 161, 162, 163, 164, 167, 170, 171, 172

Offset: 1

Author

Alexandre Wajnberg, Apr 17 2005

Keywords

• easy
• nonn

Comments

Complement of A147820. - Omar E. Pol, Nov 17 2008

m is in the sequence iff A177961(m)Vladimir Shevelev, May 16 2010

Examples

			a(1)=13 is the first number satisfying simultaneously the two rules.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A047845 and A104275.

Cf. A040040, A147820, A025583.

Cf. A010051, A002808, A099047.

Programs

Haskell

a104278 n = a104278_list !! (n-1)
a104278_list = [m | m <- [1..],
                    a010051' (2 * m - 1) == 0 && a010051' (2 * m + 1) == 0]
-- Reinhard Zumkeller, Aug 04 2015

Mathematica

Select[ Range[300], !PrimeQ[2# + 1] && !PrimeQ[2# - 1] &] (* Robert G. Wilson v, Apr 18 2005 *)
Select[Range[300],NoneTrue[2#+{1,-1},PrimeQ]&] (* The program uses the NoneTrue function from Mathematica version 10 *)  (* Harvey P. Dale, Jul 07 2015 *)

PARI

select( {is_A104278(n)=!isprime(2*n-1)&&!isprime(2*n+1)}, [1..222]) \\ M. F. Hasler, Apr 29 2024

Formula

a(n) = (A025583-1)/2. - Bill McEachen, Feb 05 2025

Extensions

More terms from Robert G. Wilson v, Apr 18 2005