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 A217001 Numbers k such that (k^2 + k + 2)/4 is prime. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS (A000217(a(n))+1)/2 is prime. LINKS Daniel Starodubtsev, Table of n, a(n) for n = 1..10000 EXAMPLE 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. 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 *) PROG (PARI) is(n)=isprime((n^2+n+2)/4) \\ Charles R Greathouse IV, Jun 13 2017 CROSSREFS Cf. A000040. Sequence in context: A327895 A096378 A342426 * A320666 A079023 A327967 Adjacent sequences:  A216998 A216999 A217000 * A217002 A217003 A217004 KEYWORD nonn,easy AUTHOR César Eliud Lozada, Sep 22 2012 STATUS approved

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Last modified January 24 08:30 EST 2022. Contains 350534 sequences. (Running on oeis4.)