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