A230775 Smallest prime number greater than or equal to the square root of n.

2, 2, 2, 2, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11

Offset

1,1

Comments

Or repeat prime(k) (prime(k)^2-prime(k-1)^2) times, with prime(0) set to 0 for k=1.

Links

Jean-Christophe Hervé, Table of n, a(n) for n = 1..10000

Formula

a(n) = A000040(A230774(n)).

Repeat prime(1) prime(1)^2 times; for k>1, repeat A000040(k) A050216(k-1) times (that is, repeat prime(k) (prime(k)^2 - prime(k-1)^2) times).

Example

a(5)=a(6)=a(7)=a(8)=a(9)=3 because prime(1)= 2 < sqrt(5 to 9) <= prime(2) = 3.

Mathematica

spn[n_]:=Module[{s=Sqrt[n]}, If[PrimeQ[s], s, NextPrime[s]]]; Array[spn, 90] (* Harvey P. Dale, Feb 10 2019 *)

Crossrefs

Cf. A230774, A050216, A056813.

Sequence in context: A135297 A176146 A171481 * A108037 A237354 A261104

Adjacent sequences: A230772 A230773 A230774 * A230776 A230777 A230778

Keyword

nonn,easy

Author

Jean-Christophe Hervé, Nov 01 2013

Status

approved