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A336374

Numbers k such that gcd(k, prime(k) + prime(k+2)) = 1.

4

1, 3, 5, 7, 11, 13, 15, 17, 19, 23, 27, 29, 31, 35, 37, 39, 41, 43, 47, 49, 53, 55, 59, 61, 63, 65, 67, 69, 71, 73, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 107, 109, 113, 115, 119, 121, 127, 129, 131, 135, 137, 139, 141, 143, 147, 149, 151

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OFFSET

1,2

COMMENTS

This sequence and A336374 partition the positive integers.

LINKS

Table of n, a(n) for n=1..61.

EXAMPLE

In the following table, p(k) = A000040(k) = prime(k).

k p(k) p(k)+p(k+2) gcd

1 2 7 1

2 3 10 2

3 5 16 1

4 7 20 4

5 11 28 1

6 13 32 2

1 and 3 are in this sequence; 2 and 4 are in A336375; 2 and 5 are in A336376; 3 and 7 are in A336377.

MATHEMATICA

p[n_] := Prime[n];

u = Select[Range[200], GCD[#, p[#] + p[# + 2]] == 1 &] (* A336374 *)

v = Select[Range[200], GCD[#, p[#] + p[# + 2]] > 1 &] (* A336375 *)

Prime[u] (* A336376 *)

Prime[v] (* A336377 *)

CROSSREFS

Cf. A000040, A336366, A336375, A336376, A336377.

Sequence in context: A210719 A353685 A322840 * A346669 A187929 A272872

Adjacent sequences: A336371 A336372 A336373 * A336375 A336376 A336377

KEYWORD

nonn

AUTHOR

Clark Kimberling, Oct 06 2020

STATUS

approved