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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

User: Daniel J. Hardisky

Daniel J. Hardisky's wiki page.

Daniel J. Hardisky has authored 2 sequences.

A220954 Primes p such that floor(sqrt(2) + sqrt(3) + sqrt(5) + ... + sqrt(p)) is prime.

Original entry on oeis.org

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
Offset: 1

Views

Author

Daniel J. Hardisky, Feb 20 2013

Keywords

Examples

			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.

Crossrefs

Cf. A062009.

Programs

  • 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
  • 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 *)
  • PARI
    s=0;forprime(p=2,1e4,if(isprime(floor(s+=sqrt(p))),print1(p", "))) \\ Charles R Greathouse IV, Feb 21 2013

A220953 Primes p such that floor(sqrt(2)) + floor(sqrt(3)) + floor(sqrt(5)) + ... + floor(sqrt(p)) is prime.

Original entry on oeis.org

3, 29, 61, 73, 127, 181, 229, 251, 281, 313, 367, 487, 503, 509, 547, 587, 599, 601, 613, 617, 659, 727, 739, 751, 797, 809, 829, 863, 881, 983, 1033, 1061, 1087, 1103, 1153, 1163, 1223, 1277, 1381, 1861, 1871, 2039, 2063, 2099, 2113, 2131, 2203, 2221
Offset: 1

Views

Author

Daniel J. Hardisky, Feb 20 2013

Keywords

Links

Crossrefs

Cf. A062048.

Programs

  • Magma
    [NthPrime(i): i in [1..400] | IsPrime(S) where S is &+[Floor(Sqrt(NthPrime(k))): k in [1..i]]]; // Bruno Berselli, Feb 21 2013
  • Mathematica
    ps = Prime[Range[1000]]; t = {}; s = 0; Do[s = s + Floor[Sqrt[p]]; If[PrimeQ[s], AppendTo[t, p]], {p, ps}]; t (* T. D. Noe, Feb 21 2013 *)
  • PARI
    s=0;forprime(p=2,1e4,if(isprime(s+=sqrtint(p)),print1(p", "))) \\ Charles R Greathouse IV, Feb 21 2013

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