A217001 Numbers k such that (k^2 + k + 2)/4 is prime.

2, 6, 9, 14, 22, 25, 30, 33, 41, 46, 49, 54, 57, 62, 86, 89, 97, 113, 118, 121, 126, 134, 142, 161, 177, 198, 201, 209, 214, 217, 222, 225, 238, 254, 265, 273, 278, 286, 294, 302, 305, 310, 313, 321, 329, 337, 342, 350, 366, 393, 414, 417, 425, 441, 449, 470

Offset: 1

Author

César Eliud Lozada, Sep 22 2012

Keywords

• nonn
• easy

Comments

(A000217(a(n))+1)/2 is prime.

Examples

			For k=2, (k^2 + k + 2)/4 = 2 is prime. Then 2 is in the sequence.
For k=6, (k^2 + k + 2)/4 = 11 is prime. Then 6 is in the sequence.
For k=5, (k^2 + k + 2)/4 = 8 is not prime. Then 5 is not in the sequence.
		

Links

• Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040.

Programs

Maple

tn := unapply(n*(n+1)/2,n):
f := unapply((t+1)/2,t):
T := []: N := []: P := []:
for k from 0 to 5000 do
  t:=tn(k):
  p := f(k):
  if p = floor(p) then
    p = floor(p):
    if isprime(p) then
      T := [op(T), t]:
      N := [op(N), k]:
      P := [op(P), p]:
    end if:
end if:
  if nops(T) = 50 then
    break:
  end if:
end do:
N := N;

Mathematica

Select[Range[500], PrimeQ[(#^2 + # + 2)/4] &] (* T. D. Noe, Sep 24 2012 *)

PARI

is(n)=isprime((n^2+n+2)/4) \\ Charles R Greathouse IV, Jun 13 2017