A221056 - OEIS

%I #13 Feb 16 2025 08:33:18

%S 1,3,5,7,8,10,12,13,14,16,17,19,20,21,23,24,26,27,28,29,31,32,33,35,

%T 36,37,38,40,41,42,43,45,46,47,49,50,51,52,53,55,56,57,58,59,60,62,63,

%U 64,65,67,68,69,70,71,73,74,75,76,77,79,80,81,82,83,84,86

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

%C A061265(a(n)) = 0;

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

%H Reinhard Zumkeller, <a href="/A221056/b221056.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LegendresConjecture.html">Legendre's Conjecture</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Legendre%27s_conjecture">Legendre's conjecture</a>

%t Select[Range[86], Ceiling[Sqrt[Prime[#]]]^2 > Prime[# + 1] &] (* _Zak Seidov_, Apr 16 2013 *)

%o (Haskell)

%o import Data.List (elemIndices)

%o a221056 n = a221056_list !! (n-1)

%o a221056_list = map (+ 1) $ elemIndices 0 a061265_list

%o (PARI) {for (n = 1, 86, ceil (sqrt (prime (n)))^2 > prime (n + 1) && print1 (n ","))} \\ _Zak Seidov_, Apr 16 2013

%Y Cf. A038107, A014085.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Apr 15 2013