A147820 -id:A147820 - cp's OEIS frontend

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

Alexandre Wajnberg, Apr 17 2005

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

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

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

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

Intersection of A047845 and A104275.
Cf. A040040, A147820, A025583.
Cf. A010051, A002808, A099047.

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

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 *)

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

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

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

A309120 a(n) is the least k > 1 such that n*k is adjacent to a prime.

Original entry on oeis.org

2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 4, 2, 2, 3, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 6, 3, 6, 5, 2, 2, 2, 2, 4, 2, 2, 2, 4, 5, 4, 2, 2, 2, 4, 2, 2, 3, 2, 2, 2, 2, 6, 2, 2, 3, 2, 2, 2, 3, 4, 3

Offset: 1

Robert Israel, Jul 17 2019

nonn

If n is odd then a(n) is even.

a(n) exists by Dirichlet's theorem on primes in arithmetic progressions.

			a(13)=4 because 4*13+1=53 is prime but none of 2*13-1,2*13+1,3*13-1,3*13+1 are primes.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A307833, A104278, A147820.

f:= proc(m) local k;
  for k from 2 by 1+(m mod 2) do
    if isprime(k*m-1) or isprime(k*m+1) then return k fi
  od
end proc:
map(f, [$1..100]);

a[n_]:=Module[{k=2},While[Not[PrimeQ[k*n-1]||PrimeQ[k*n+1]],k++];k];
a/@Range[94] (* Ivan N. Ianakiev, Jul 18 2019 *)

a(n) = my(k=2); while (!isprime(n*k+1) && !isprime(n*k-1), k++); k; \\ Michel Marcus, Jul 19 2019

a(A104278(n)) > 2 and a(A147820(n)) = 2. - Ivan N. Ianakiev, Jul 18 2019

cp's OEIS Frontend

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

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