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

%I A217001 #20 Mar 24 2020 06:38:27
%S A217001 2,6,9,14,22,25,30,33,41,46,49,54,57,62,86,89,97,113,118,121,126,134,
%T A217001 142,161,177,198,201,209,214,217,222,225,238,254,265,273,278,286,294,
%U A217001 302,305,310,313,321,329,337,342,350,366,393,414,417,425,441,449,470
%N A217001 Numbers k such that (k^2 + k + 2)/4 is prime.
%C A217001 (A000217(a(n))+1)/2 is prime.
%H A217001 Daniel Starodubtsev, <a href="/A217001/b217001.txt">Table of n, a(n) for n = 1..10000</a>
%e A217001 For k=2, (k^2 + k + 2)/4 = 2 is prime. Then 2 is in the sequence.
%e A217001 For k=6, (k^2 + k + 2)/4 = 11 is prime. Then 6 is in the sequence.
%e A217001 For k=5, (k^2 + k + 2)/4 = 8 is not prime. Then 5 is not in the sequence.
%p A217001 tn := unapply(n*(n+1)/2,n):
%p A217001 f := unapply((t+1)/2,t):
%p A217001 T := []: N := []: P := []:
%p A217001 for k from 0 to 5000 do
%p A217001   t:=tn(k):
%p A217001   p := f(k):
%p A217001   if p = floor(p) then
%p A217001     p = floor(p):
%p A217001     if isprime(p) then
%p A217001       T := [op(T), t]:
%p A217001       N := [op(N), k]:
%p A217001       P := [op(P), p]:
%p A217001     end if:
%p A217001 end if:
%p A217001   if nops(T) = 50 then
%p A217001     break:
%p A217001   end if:
%p A217001 end do:
%p A217001 N := N;
%t A217001 Select[Range[500], PrimeQ[(#^2 + # + 2)/4] &] (* _T. D. Noe_, Sep 24 2012 *)
%o A217001 (PARI) is(n)=isprime((n^2+n+2)/4) \\ _Charles R Greathouse IV_, Jun 13 2017
%Y A217001 Cf. A000040.
%K A217001 nonn,easy
%O A217001 1,1
%A A217001 _César Eliud Lozada_, Sep 22 2012