A296058 Numbers k such that floor((3*k - 1)/2) is prime.

2, 4, 5, 8, 9, 12, 13, 16, 20, 21, 25, 28, 29, 32, 36, 40, 41, 45, 48, 49, 53, 56, 60, 65, 68, 69, 72, 73, 76, 85, 88, 92, 93, 100, 101, 105, 109, 112, 116, 120, 121, 128, 129, 132, 133, 141, 149, 152, 153, 156, 160, 161, 168, 172, 176, 180, 181, 185, 188, 189

Offset

1,1

Comments

Numbers k such that A001651(k) is prime.

This sequence is infinite because values of the form floor((3*k-1)/2) include all primes except 3.

Links

Iain Fox, Table of n, a(n) for n = 1..10000

Formula

a(n) = floor((2*prime(n+1) + 2)/3).

a(n) = A004523(A000040(n+1) + 1).

Example

Floor((3*4 - 1)/2) = 5 is prime, so 4 is a term.
Floor((3*5 - 1)/2) = 7 is prime, so 5 is a term.
Floor((3*6 - 1)/2) = 8 is not prime, so 6 is not a term.

Mathematica

Select[Range[200], PrimeQ@ Floor[(3 # - 1)/2] &] (* or *)
Array[Floor[2 (Prime[# + 1] + 1)/3] &, 60] (* Michael De Vlieger, Dec 09 2017 *)

Prog

(PARI) is(n) = isprime(floor((3*n-1)/2))
(PARI) a(n) = floor((2*prime(n+1) + 2)/3)
(PARI) lista(nn) = forprime(p=3, nn, print1(floor((2*p + 2)/3), ", "))

Crossrefs

Characteristic function: A296028.

Cf. A000040, A001651.

Sequence in context: A346111 A286805 A188072 * A189205 A137169 A348458

Adjacent sequences: A296055 A296056 A296057 * A296059 A296060 A296061

Keyword

nonn

Author

Iain Fox, Dec 03 2017

Status

approved