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URL: https://oeis.org/A336368

⇱ A336368 - OEIS

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A336368

Primes p(n) such that gcd(n, prime(n)+prime(n+1)) = 1.

4

2, 11, 17, 23, 31, 41, 59, 67, 73, 83, 97, 109, 127, 157, 167, 179, 191, 211, 227, 233, 241, 277, 283, 331, 353, 367, 389, 401, 431, 439, 461, 467, 499, 509, 523, 547, 563, 587, 599, 607, 617, 631, 653, 661, 677, 691, 709, 727, 739, 751, 773, 797, 829, 859

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OFFSET

1,1

COMMENTS

This sequence and A336369 partition the set of primes.

LINKS

Table of n, a(n) for n=1..54.

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

Cf. A000040, A336366, A336367, A336369.

Sequence in context: A255609 A105840 A243960 * A282509 A225590 A060427

Adjacent sequences: A336365 A336366 A336367 * A336369 A336370 A336371

KEYWORD

nonn

AUTHOR

Clark Kimberling, Oct 04 2020

STATUS

approved