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URL: https://oeis.org/A336373

⇱ A336373 - OEIS

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A336373
Primes prime(k) such that gcd(k, prime(k)+prime(k-1)) > 1.
4
7, 13, 19, 23, 29, 37, 41, 43, 47, 53, 61, 71, 73, 79, 89, 101, 103, 107, 113, 131, 139, 151, 163, 167, 173, 181, 193, 197, 199, 223, 229, 233, 239, 251, 263, 269, 271, 281, 293, 307, 311, 313, 317, 337, 347, 349, 359, 373, 383, 397, 409, 419, 421, 433, 443
OFFSET
1,1
COMMENTS
This sequence and A336372 partition the set of odd primes.
EXAMPLE
In the following table, p(n) = A000040(n) = prime(n).
n p(n) p(n)+p(n-1) gcd
2 3 5 1
3 5 8 1
4 7 12 4
5 11 18 1
6 13 24 6
2 and 3 are in A336370; 4 and 6 are in A336371; 3 and 5 are in A336372; 7 and 13 are in this sequence.
MATHEMATICA
p[n_] := Prime[n];
u = Select[Range[2, 200], GCD[#, p[#] + p[# - 1]] == 1 &] (* A336370 *)
v = Select[Range[2, 200], GCD[#, p[#] + p[# - 1]] > 1 &] (* A336371 *)
Prime[u] (* A336372 *)
Prime[v] (* A336373 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Oct 05 2020
EXTENSIONS
Offset corrected by Mohammed Yaseen, Jul 16 2023
STATUS
approved