A247485 Integer part of 2*sqrt(prime(n)) + 1.

3, 4, 5, 6, 7, 8, 9, 9, 10, 11, 12, 13, 13, 14, 14, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 21, 21, 21, 21, 22, 23, 23, 24, 24, 25, 25, 26, 26, 26, 27, 27, 27, 28, 28, 29, 29, 30, 30, 31, 31, 31, 31, 32, 32, 33, 33, 33, 33, 34, 34, 34, 35, 36, 36, 36, 36, 37

Offset: 1

Author

Reinhard Zumkeller, Sep 20 2014

Keywords

• nonn

Comments

A117767(n) = 2*floor(sqrt(prime(n))) + 1 <= a(n);

a(A247514(n)) = A117767(A247514(n)); a(A247515(n)) > A117767(A247515(n)).

Andrica's conjecture: a(n) <= A001223(n).

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Andrica's Conjecture
• Eric Weisstein's World of Mathematics, Legendre's Conjecture
• Wikipedia, Andrica's conjecture

Crossrefs

Cf. A117767, A001223, A000040, A000006, A247514, A247515.

Programs

Haskell

a247485 = (+ 1) . floor . (* 2) . sqrt . fromIntegral . a000040

Mathematica

Floor[2Sqrt[Prime[Range[70]]]+1] (* Harvey P. Dale, Sep 04 2020 *)

PARI

a(n) = 1+sqrtint(4*prime(n)); \\ Michel Marcus, Aug 26 2021