A073426 Number of primes between n-th prime and n-th composite or number of primes that are >=Min[prime(n),c(n)] and are < Max[prime(n),c(n)].

2, 2, 2, 1, 1, 1, 1, 2, 3, 3, 3, 4, 5, 5, 6, 7, 8, 9, 9, 9, 10, 11, 12, 13, 13, 14, 15, 15, 15, 16, 17, 17, 18, 19, 20, 21, 21, 22, 23, 24, 25, 25, 25, 26, 27, 28, 29, 29, 30, 31, 31, 31, 32, 33, 34, 35, 35, 36, 37, 37, 38, 39, 40, 41, 41, 42, 43, 44, 45, 46, 47, 47, 48, 49, 49, 49

Offset

1,1

Links

Table of n, a(n) for n=1..76.

Formula

a(n)=A000720[A000040(n)]-A000720[A002808(n)], for n>=5; a(n)=A000720[A002808(n)]-n+1 for n=1, 2, 3, 4.

Example

n=4: in range {p(4)=11 and c(4)=10} 1 prime was found, a(4)=1; n=25: in range {p(25)=97 and c(25)=38} 13 primes, {41,43,..,97} were found, so a(25)=13.

Mathematica

c[x_] := FixedPoint[x+PrimePi[ # ]+1&, x] Table[PrimePi[c[w]]-w+1, {w, 1, 4}] Table[w-PrimePi[c[w]], {w, 5, 128}]

Crossrefs

Cf. A065890, A073425, A000720, A002808.

Sequence in context: A227739 A047971 A029432 * A232439 A346118 A309797

Adjacent sequences: A073423 A073424 A073425 * A073427 A073428 A073429

Keyword

nonn

Author

Labos Elemer, Jul 31 2002

Status

approved