OFFSET
1,1
COMMENTS
LINKS
Robert Price, Table of n, a(n) for n = 1..170
Carlos Rivera, Conjecture 30. The Firoozbakht Conjecture PrimePuzzles.net.
A. Kourbatov, Verification of the Firoozbakht conjecture for primes up to four quintillion, arXiv:1503.01744 [math.NT], 2015
Wikipedia, Firoozbakht's conjecture
EXAMPLE
12 is in the sequence since there exists only three primes p where, prime(12) < p < prime(12)^(1 + 1/12). Note that prime(12) = 37, 37^(1 + 1/12) ~ 49.99 and 37 < 41 < 43 < 47 < 49.99.
MAPLE
N:= 10^5: # to get all terms where prime(n)^(1+1/n) < N
Primes:= select(isprime, [2, seq(2*i+1, i=1..floor((N+1)/2))]):
filter:= proc(n) local t; t:= Primes[n]^(n+1); Primes[n+3]^n <= t and Primes[n+4]^n > t end proc:
select(filter, [$1..nops(Primes)-4]); # Robert Israel, Mar 23 2015
MATHEMATICA
np[n_] := (a = Prime[n]; b = a^(1 + 1/n); Length[Select[Range[a + 1, b], PrimeQ]]); Select[Range[10000], np[#] == 3 &]
PROG
(Haskell)
a246781 n = a246781_list !! (n-1)
a246781_list = filter ((== 3) . a182134) [1..]
-- Reinhard Zumkeller, Nov 17 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Farideh Firoozbakht, Oct 12 2014
EXTENSIONS
a(43)-a(50) from Robert Price, Oct 24 2014
STATUS
approved