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A336381
Primes p(n) such that gcd(n, prime(n-1)+prime(n+1)) > 1.
4
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
1,1
LINKS
EXAMPLE
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.
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 *)
PROG
(PARI) for(n=2, 200, if(gcd(n, prime(n-1)+prime(n+1))>1, print1(prime(n), ", "))) \\ Derek Orr, Nov 23 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Oct 25 2020
EXTENSIONS
Offset changed by Robert Israel, Dec 08 2020
STATUS
approved