OFFSET
1,3
COMMENTS
Number of primes between successive even semiprimes. [Juri-Stepan Gerasimov, May 01 2010]
From Peter Munn, Jun 01 2023: (Start)
First differences of A020900.
A080192 lists prime(n) corresponding to the zero terms.
A104380(k) is prime(n) corresponding to the first occurrence of k as a term.
If a(n) is nonzero, A059786(n) is the smallest and A059788(n+1) the largest of the a(n) enumerated primes. In the tree of primes described in A290183, these primes label the child nodes of prime(n).
Conjecture: the asymptotic proportions of 0's, 1's, ... , k's, ... are 1/3, 2/9, ... , 2^k/3^(k+1), ... .
(End)
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
V. Shevelev, On critical small intervals containing primes, arXiv:0908.2319 [math.NT], 2009.
FORMULA
EXAMPLE
a(15)=3 because there are 3 primes between the doubles of the 15th and 16th primes, that is between 2*47 and 2*53.
MATHEMATICA
Table[PrimePi[2 Prime[n+1]]-PrimePi[2 Prime[n]], {n, 150}] (* Zak Seidov *)
Differences[PrimePi[2 Prime[Range[110]]]] (* Harvey P. Dale, Oct 29 2022 *)
PROG
(Haskell)
a102820 n = a102820_list !! (n-1)
a102820_list = map (sum . (map a010051)) $
zipWith enumFromTo a100484_list (tail a100484_list)
-- Reinhard Zumkeller, Apr 29 2012
(PARI) a(n) = primepi(2*prime(n+1)) - primepi(2*prime(n)); \\ Michel Marcus, Sep 22 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Ali A. Tanara (tanara(AT)khayam.ut.ac.ir), Feb 27 2005
EXTENSIONS
More terms from Zak Seidov, Feb 28 2005
STATUS
approved