A221056 Numbers k such that there is no square between prime(k) and prime(k+1).

1, 3, 5, 7, 8, 10, 12, 13, 14, 16, 17, 19, 20, 21, 23, 24, 26, 27, 28, 29, 31, 32, 33, 35, 36, 37, 38, 40, 41, 42, 43, 45, 46, 47, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 62, 63, 64, 65, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 79, 80, 81, 82, 83, 84, 86

Offset: 1

Author

Reinhard Zumkeller, Apr 15 2013

Keywords

• nonn

Comments

A061265(a(n)) = 0;

a(n) = A049084(A224363(n)); A000040(a(n)) = A224363(n).

Links

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

Crossrefs

Cf. A038107, A014085.

Programs

Haskell

import Data.List (elemIndices)
a221056 n = a221056_list !! (n-1)
a221056_list = map (+ 1) $ elemIndices 0 a061265_list

Mathematica

Select[Range[86], Ceiling[Sqrt[Prime[#]]]^2 > Prime[# + 1] &] (* Zak Seidov, Apr 16 2013 *)

PARI

{for (n = 1, 86, ceil (sqrt (prime (n)))^2 > prime (n + 1) && print1 (n ","))} \\ Zak Seidov, Apr 16 2013