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A336369
Primes p(n) such that gcd(n, prime(n)+prime(n+1)) > 1.
4
3, 5, 7, 13, 19, 29, 37, 43, 47, 53, 61, 71, 79, 89, 101, 103, 107, 113, 131, 137, 139, 149, 151, 163, 173, 181, 193, 197, 199, 223, 229, 239, 251, 257, 263, 269, 271, 281, 293, 307, 311, 313, 317, 337, 347, 349, 359, 373, 379, 383, 397, 409, 419, 421, 433
OFFSET
1,1
COMMENTS
This sequence and A336368 partition the set of primes.
EXAMPLE
In the following table, p(n) = A000040(n) = prime(n).
n p(n) p(n)+p(n+1) gcd
1 2 5 1
2 3 8 4
3 5 12 3
4 7 18 2
5 11 24 1
6 13 30 6
1 and 5 are in A336366; 2 and 3 are in A336367; 2 and 11 are in A336368; 3 and 5 are in A336369.
MATHEMATICA
p[n_] := Prime[n];
u = Select[Range[200], GCD[#, p[#] + p[# + 1]] == 1 &] (* A336366 *)
v = Select[Range[200], GCD[#, p[#] + p[# + 1]] > 1 &] (* A336367 *)
Prime[u] (* A336368 *)
Prime[v] (* A336369 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Oct 04 2020
STATUS
approved