A220954 - OEIS

A220954

Primes p such that floor(sqrt(2) + sqrt(3) + sqrt(5) + ... + sqrt(p)) is prime.

3, 5, 11, 17, 19, 73, 83, 109, 179, 211, 269, 271, 283, 373, 557, 571, 587, 607, 661, 677, 809, 953, 997, 1013, 1031, 1033, 1087, 1093, 1151, 1171, 1217, 1249, 1289, 1301, 1427, 1439, 1447, 1453, 1549, 1613, 1621, 1867, 1877, 1949, 2179, 2347, 2393, 2467

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OFFSET

1,1

LINKS

Robert Israel, Table of n, a(n) for n = 1..723

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.

MAPLE

N:= 3000: # for terms <= N

P:= select(isprime, [2, seq(i, i=3..10^5, 2)]):

S:= map(floor, ListTools:-PartialSums(map(sqrt, P))):

P[select(t -> isprime(S[t]), [$1..nops(P)])]; # Robert Israel, Apr 19 2026

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

Cf. A062009.

Sequence in context: A268155 A199217 A141165 * A155937 A050566 A032382

Adjacent sequences: A220951 A220952 A220953 * A220955 A220956 A220957

KEYWORD

nonn

AUTHOR

Daniel J. Hardisky, Feb 20 2013

STATUS

approved