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%I #18 Sep 08 2022 08:46:04
%S 3,5,11,17,19,73,83,109,179,211,269,271,283,373,557,571,587,607,661,
%T 677,809,953,997,1013,1031,1033,1087,1093,1151,1171,1217,1249,1289,
%U 1301,1427,1439,1447,1453,1549,1613,1621,1867,1877,1949,2179,2347,2393,2467
%N Primes p such that floor(sqrt(2) + sqrt(3) + sqrt(5) + ... + sqrt(p)) is prime.
%e 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.
%t 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 *)
%t With[{prs=Prime[Range[400]]},Select[prs,PrimeQ[Floor[Total[Sqrt[Take[ prs, PrimePi[ #]]]]]]&]] (* _Harvey P. Dale_, Feb 25 2013 *)
%o (PARI) s=0;forprime(p=2,1e4,if(isprime(floor(s+=sqrt(p))),print1(p", "))) \\ _Charles R Greathouse IV_, Feb 21 2013
%o (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
%Y Cf. A062009.
%K nonn
%O 1,1
%A _Daniel J. Hardisky_, Feb 20 2013
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