A127441 - OEIS

A127441

Numbers n such that between n and n+sqrt(n) there are no primes.

3, 7, 8, 13, 23, 24, 31, 113, 114, 115, 116

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OFFSET

1,1

COMMENTS

If Oppermann's conjecture is true, then all terms are nonsquares. Data from A002386 and A005250 show that a(12) > 6787988999657777797 if it exists. Most likely there are no further terms. - Chai Wah Wu, Mar 08 2019

LINKS

Table of n, a(n) for n=1..11.

Wikipedia, Oppermann's conjecture

MATHEMATICA

a = {}; Do[If[PrimePi[x + x^(1/2)] - PrimePi[x] == 0, AppendTo[a, x]], {x, 1, 249900000000000}]; a

PROG

(PARI) isok(n) = primepi(n+sqrtint(n)) == primepi(n); \\ Michel Marcus, Nov 07 2013

CROSSREFS

Cf. A000720, A002386, A005250, A028392.

Sequence in context: A252496 A279517 A106474 * A067064 A093722 A309745

Adjacent sequences: A127438 A127439 A127440 * A127442 A127443 A127444

KEYWORD

nonn,more

AUTHOR

Artur Jasinski, Jan 14 2007

STATUS

approved