A245508 Smallest double square (cf. A001105) greater than n-th prime.

2, 8, 8, 8, 18, 18, 18, 32, 32, 32, 32, 50, 50, 50, 50, 72, 72, 72, 72, 72, 98, 98, 98, 98, 98, 128, 128, 128, 128, 128, 128, 162, 162, 162, 162, 162, 162, 200, 200, 200, 200, 200, 200, 200, 200, 200, 242, 242, 242, 242, 242, 242, 242, 288, 288, 288, 288

Offset: 1

Author

Reinhard Zumkeller, Jul 25 2014

Keywords

• nonn

Comments

For n > 2: prime(n) < a(n) < 2*prime(n) and a(n) = A245499(A000040(n),2).

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A001105, A145445.

Programs

Haskell

import Data.List (genericIndex)
a245508 n = genericIndex a245508_list (n-1)
a245508_list = f a000040_list a001105_list where
   f ps'@ (p:ps) xs'@(x:xs) = if p <= x then x : f ps xs' else f ps' xs

Mathematica

Module[{nn=60,ds},ds=2 Range[0,Ceiling[Sqrt[Prime[nn]]]]^2;Join[ {2},Table[ SelectFirst[ds,#>Prime[n]&],{n,2,nn}]]] (* Harvey P. Dale, Jan 07 2020 *)

PARI

a(n) = my(k=prime(n)+(n!=1)); while (! issquare(k/2), k+=2); k; \\ Michel Marcus, Jan 24 2022