A336381 - OEIS

%I #16 Dec 07 2022 12:27:15

%S 7,11,13,19,23,29,31,37,43,47,53,61,71,73,79,89,97,101,107,113,131,

%T 137,139,149,151,163,167,173,181,193,199,223,229,233,239,251,263,269,

%U 271,281,293,311,317,337,349,359,373,379,383,397,409,421,433,443,449

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

%H Robert Israel, <a href="/A336381/b336381.txt">Table of n, a(n) for n = 1..10000</a>

%e In the following table, P(n) = A000040(n) = prime(n).

%e   n    P(n)   P(n-1)+P(n+1)   gcd

%e   2     3          7           1

%e   3     5         10           1

%e   4     7         16           4

%e   5    11         20           5

%e   6    13         28           2

%e 2 and 3 are in A336378; 4 and 5 are in A336379; 3 and 5 are in A336380; 7 and 11 are in A336381.

%p q:= 2: r:= 3:

%p R:= NULL: count:= 0:

%p for n from 2 while count < 100 do

%p   p:= q; q:= r; r:= nextprime(r);

%p   if igcd(n,p+r) > 1 then count:= count+1; R:= R, q; fi

%p od:

%p R; # _Robert Israel_, Dec 08 2020

%t p[n_] := Prime[n];

%t u = Select[Range[2, 200], GCD[#, p[# - 1] + p[# + 1]] == 1 &]  (* A336378 *)

%t v = Select[Range[2, 200], GCD[#, p[# - 1] + p[# + 1]] > 1 &]   (* A336379 *)

%t Prime[u]  (* A336380 *)

%t Prime[v]  (* A336381 *)

%t Select[Partition[Prime[Range[100]],3,1],GCD[PrimePi[#[[2]]],#[[1]]+#[[3]]]>1&][[All,2]] (* _Harvey P. Dale_, Dec 07 2022 *)

%o (PARI) for(n=2,200,if(gcd(n,prime(n-1)+prime(n+1))>1,print1(prime(n),", "))) \\ _Derek Orr_, Nov 23 2020

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

%K nonn

%O 1,1

%A _Clark Kimberling_, Oct 25 2020

%E Offset changed by _Robert Israel_, Dec 08 2020