A336381 Primes p(n) such that gcd(n, prime(n-1)+prime(n+1)) > 1.

7, 11, 13, 19, 23, 29, 31, 37, 43, 47, 53, 61, 71, 73, 79, 89, 97, 101, 107, 113, 131, 137, 139, 149, 151, 163, 167, 173, 181, 193, 199, 223, 229, 233, 239, 251, 263, 269, 271, 281, 293, 311, 317, 337, 349, 359, 373, 379, 383, 397, 409, 421, 433, 443, 449

Offset: 1

Author

Clark Kimberling, Oct 25 2020

Keywords

• nonn

Examples

			In the following table, P(n) = A000040(n) = prime(n).
  n    P(n)   P(n-1)+P(n+1)   gcd
  2     3          7           1
  3     5         10           1
  4     7         16           4
  5    11         20           5
  6    13         28           2
2 and 3 are in A336378; 4 and 5 are in A336379; 3 and 5 are in A336380; 7 and 11 are in A336381.
		

Links

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

Crossrefs

Cf. A000040, A048448, A336366, A336378, A336379, A336380.

Programs

Maple

q:= 2: r:= 3:
R:= NULL: count:= 0:
for n from 2 while count < 100 do
  p:= q; q:= r; r:= nextprime(r);
  if igcd(n,p+r) > 1 then count:= count+1; R:= R, q; fi
od:
R; # Robert Israel, Dec 08 2020

Mathematica

p[n_] := Prime[n];
u = Select[Range[2, 200], GCD[#, p[# - 1] + p[# + 1]] == 1 &]  (* A336378 *)
v = Select[Range[2, 200], GCD[#, p[# - 1] + p[# + 1]] > 1 &]   (* A336379 *)
Prime[u]  (* A336380 *)
Prime[v]  (* A336381 *)
Select[Partition[Prime[Range[100]],3,1],GCD[PrimePi[#[[2]]],#[[1]]+#[[3]]]>1&][[All,2]] (* Harvey P. Dale, Dec 07 2022 *)

PARI

for(n=2,200,if(gcd(n,prime(n-1)+prime(n+1))>1,print1(prime(n),", "))) \\ Derek Orr, Nov 23 2020

Extensions

Offset changed by Robert Israel, Dec 08 2020