A137404 - OEIS

A137404

a(n) = ceiling(10*(prime(n+1)-prime(n))/(2*floor(sqrt(prime(n)*log(prime(n)))))).

5, 10, 5, 7, 2, 4, 2, 3, 4, 2, 3, 2, 1, 2, 3, 3, 1, 2, 2, 1, 2, 2, 2, 3, 1, 1, 1, 1, 1, 4, 1, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..100.

Andrew Granville, Harald Cramer and the Distribution of Prime Numbers

MATHEMATICA

a = Flatten[Table[10*x /. Solve[Prime[n + 1] -Prime[n] - x*2*Floor[Sqrt[Prime[n]*Log[Prime[n]]]] == 0, x], {n, 1, 100}]]; Ceiling[a]

PROG

(PARI) a(n) = ceil(10*(prime(n+1)-prime(n))/ (2*floor(sqrt(prime(n)*log(prime(n)))))); \\ Michel Marcus, Oct 15 2020

CROSSREFS

Cf. A000040.