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A336372
Primes prime(k) such that gcd(k, prime(k) + prime(k-1)) = 1.
3
3, 5, 11, 17, 31, 59, 67, 83, 97, 109, 127, 137, 149, 157, 179, 191, 211, 227, 241, 257, 277, 283, 331, 353, 367, 379, 389, 401, 431, 439, 449, 461, 467, 509, 547, 563, 587, 599, 607, 617, 653, 691, 709, 739, 751, 773, 797, 823, 829, 859, 877, 907, 919, 947
OFFSET
1,1
COMMENTS
This sequence and A336373 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
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] (* this sequence *)
Prime[v] (* A336373 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Oct 05 2020
EXTENSIONS
Offset corrected by Mohammed Yaseen, Jun 02 2023
STATUS
approved