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A336379
Numbers k such that gcd(k, prime(k-1) + prime(k+1)) > 1.
3
4, 5, 6, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 46, 48, 50, 51, 52, 54, 56, 57, 58, 60, 62, 64, 66, 68, 70, 72, 74, 75, 76, 78, 80, 82, 84, 86, 87, 88, 90, 92, 94, 96, 98, 99, 100, 102, 104
OFFSET
1,1
EXAMPLE
In the following table, p(k) = A000040(k) = prime(k).
k p(k) p(k-1)+p(k+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 this sequence; 3 and 5 are in A336380; 7 and 11 are in A336381.
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 &] (* this sequence *)
Prime[u] (* A336380 *)
Prime[v] (* A336381 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Oct 06 2020
EXTENSIONS
Offset corrected by Mohammed Yaseen, Jul 16 2023
STATUS
approved