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A224363 Primes p such that there are no squares between p and the prime following p. 2
2, 5, 11, 17, 19, 29, 37, 41, 43, 53, 59, 67, 71, 73, 83, 89, 101, 103, 107, 109, 127, 131, 137, 149, 151, 157, 163, 173, 179, 181, 191, 197, 199, 211, 227, 229, 233, 239, 241, 257, 263, 269, 271, 277, 281, 293, 307, 311, 313, 331, 337, 347, 349, 353, 367, 373 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Legendre's Conjecture states that there is a prime between n^2 and (n+1)^2 for every integer n > 0 and thus that between two adjacent primes there can be at most one square. As of April 2013, the conjecture is still unproved.

a(n) = A000040(A221056(n)). - Reinhard Zumkeller, Apr 15 2013

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

EXAMPLE

5 is a term because there are no squares between the adjacent primes 5 and 7.

MATHEMATICA

Select[Prime[Range[60]], Floor[Sqrt[NextPrime[#]]] == Floor[Sqrt[#]] &] (* Giovanni Resta, Apr 10 2013 *)

PROG

(Haskell)

a224363 = a000040 . a221056  -- Reinhard Zumkeller, Apr 15 2013

CROSSREFS

Cf. A061265, A014085.

Sequence in context: A166744 A080165 A239712 * A307508 A063535 A091653

Adjacent sequences:  A224360 A224361 A224362 * A224364 A224365 A224366

KEYWORD

nonn

AUTHOR

César Aguilera, Apr 04 2013

EXTENSIONS

Corrected and edited by Giovanni Resta, Apr 10 2013

STATUS

approved

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Last modified October 20 20:24 EDT 2019. Contains 328273 sequences. (Running on oeis4.)