OFFSET
1,1
EXAMPLE
Floor(sqrt(2)+sqrt(3)+sqrt(5)+ ... +sqrt(11)+sqrt(13)+sqrt(17)) = 19 which is prime, so 17 is a member of this sequence.
MATHEMATICA
ps = Prime[Range[1000]]; t = {}; s = 0; Do[s = s + Sqrt[p]; If[PrimeQ[Floor[s]], AppendTo[t, p]], {p, ps}]; t (* T. D. Noe, Feb 21 2013 *)
With[{prs=Prime[Range[400]]}, Select[prs, PrimeQ[Floor[Total[Sqrt[Take[ prs, PrimePi[ #]]]]]]&]] (* Harvey P. Dale, Feb 25 2013 *)
PROG
(PARI) s=0; forprime(p=2, 1e4, if(isprime(floor(s+=sqrt(p))), print1(p", "))) \\ Charles R Greathouse IV, Feb 21 2013
(Magma) [NthPrime(i): i in [1..400] | IsPrime(Floor(S)) where S is &+[Sqrt(NthPrime(k)): k in [1..i]]]; // Bruno Berselli, Feb 21 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Daniel J. Hardisky, Feb 20 2013
STATUS
approved