A104380 -id:A104380 - cp's OEIS frontend

A102820 Number of primes between 2prime(n) and 2prime(n+1), where prime(n) is the n-th prime.

1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 3, 1, 1, 1, 3, 3, 0, 2, 2, 0, 3, 1, 2, 4, 2, 0, 1, 0, 1, 6, 1, 3, 1, 3, 0, 3, 1, 1, 1, 3, 1, 3, 1, 1, 1, 4, 4, 1, 1, 2, 1, 1, 3, 2, 2, 0, 1, 1, 1, 1, 3, 6, 2, 0, 1, 6, 1, 3, 0, 1, 1, 3, 2, 2, 1, 2, 1, 1, 2, 4, 1, 3, 1, 1, 2, 1, 2, 1, 0, 1, 4, 2, 1, 3, 0, 2, 5, 0, 5, 3, 3, 2, 1, 0, 2

Offset: 1

Ali A. Tanara (tanara(AT)khayam.ut.ac.ir), Feb 27 2005

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)

			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.

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.

Sequences with related analysis: A020900, A059786, A059788, A080192, A104380, A290183.
Cf. A104272, A080359. [Vladimir Shevelev, Aug 24 2009]
Cf. A100484, A010051.
Sequences with similar definitions: A104289, A217564.

a102820 n = a102820_list !! (n-1)
a102820_list =  map (sum . (map a010051)) $
   zipWith enumFromTo a100484_list (tail a100484_list)
-- Reinhard Zumkeller, Apr 29 2012

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 *)

a(n) = primepi(2*prime(n+1)) - primepi(2*prime(n)); \\ Michel Marcus, Sep 22 2017

a(n) = A020900(n+1) - A020900(n). - Peter Munn, Jun 01 2023

More terms from Zak Seidov, Feb 28 2005

A215238 Prime(A215237).

Original entry on oeis.org

2, 3, 113, 1637, 2971, 44293, 305663, 1133071, 370261, 1357201, 46006769, 268119517, 291057379, 3429782117, 10502593103, 10926444583, 87241770619, 226751019497, 1901687257447

Offset: 0

T. D. Noe, Oct 11 2012

We use offset 0 because A215237 uses that offset.

a(n) is least prime(k) such that there are exactly n primes between prime(k)/2 and prime(k+1)/2. - Peter Munn, Oct 22 2017

Cf. A000040, A080192, A104380, A215237.

t = Table[PrimePi[Prime[n + 1]/2] - PrimePi[Prime[n]/2], {n, 100000}]; t2 = Flatten[Table[Position[t, n, 1, 1], {n, 0, 8}]]; Prime[t2]

a(n) = A000040(A215237(n)).

a(14)-a(18) from Donovan Johnson, Oct 13 2012

cp's OEIS Frontend

A102820 Number of primes between 2prime(n) and 2prime(n+1), where prime(n) is the n-th prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

Mathematica

PARI

Formula

Extensions

A215238 Prime(A215237).

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

Formula

Extensions

cp's OEIS Frontend

A102820 Number of primes between 2*prime(n) and 2*prime(n+1), where prime(n) is the n-th prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

Mathematica

PARI

Formula

Extensions

A215238 Prime(A215237).

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

Formula

Extensions

A102820 Number of primes between 2prime(n) and 2prime(n+1), where prime(n) is the n-th prime.