A096501 -id:A096501 - cp's OEIS frontend

A096500 Let f(n) = smallest prime > n; a(n) = f(n+1) - f(n).

1, 2, 0, 2, 0, 4, 0, 0, 0, 2, 0, 4, 0, 0, 0, 2, 0, 4, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 0, 6, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 4, 0, 0, 0, 6, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 0, 6, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 6, 0, 0, 0, 0, 0, 4, 0, 0, 0, 6, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 4, 0, 0, 0

Offset: 1

Labos Elemer, Jul 09 2004

nonn

Antti Karttunen, Table of n, a(n) for n = 1..30000
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Cf. A000720, A001223, A010051, A096501, A175851.
First differences of A151800.
Cf. also A109578.

seq(nextprime(n+1)-nextprime(n),n=1..250); # Muniru A Asiru, Jan 03 2019

Mathematica
```
<Michael De Vlieger, Jan 03 2019 *)
```

A151800(n) = nextprime(1+n);
A096500(n) = (A151800(1+n)-A151800(n)); \\ Antti Karttunen, Jan 03 2019

From Antti Karttunen, Jan 03 2019: (Start)
a(n) = A151800(n+1) - A151800(n).
a(n) = A010051(1+n) * A001223(A000720(1+n)).
(End)

A109578 a(n) = (pi(n+1)-pi(n)) * (prime(n+1)-prime(n)), where pi(k) is the number of prime numbers less than or equal to k (= A000720(k)) and prime(k) is the k-th prime number (= A000040(k)).

Original entry on oeis.org

1, 2, 0, 4, 0, 4, 0, 0, 0, 2, 0, 4, 0, 0, 0, 6, 0, 6, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 14, 0, 0, 0, 0, 0, 6, 0, 0, 0, 6, 0, 10, 0, 0, 0, 12, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 6, 0, 2, 0, 0, 0, 0, 0, 14, 0, 0, 0, 4, 0, 8, 0, 0, 0, 0, 0, 4, 0, 0, 0, 10, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 6, 0, 6, 0, 0

Offset: 1

Roger L. Bagula, Jun 29 2005

nonn

Antti Karttunen, Table of n, a(n) for n = 1..20000

Cf. A001223, A010051.

Cf. also A096500, A096501.

with(numtheory): a:=n->(pi(n+1)-pi(n))*(ithprime(n+1)-ithprime(n)): seq(a(n),n=1..160);

an = Table[(PrimePi[n + 1] - PrimePi[n])*(Prime[n + 1] - Prime[n]), {n, 1, 200}]

A109578(n) = ((primepi(n+1)-primepi(n)) * (prime(n+1)-prime(n))); \\ Antti Karttunen, Jan 03 2019

a(n) = (A010051(1+n) * A001223(n)). - Antti Karttunen, Jan 03 2019

cp's OEIS Frontend

A096500 Let f(n) = smallest prime > n; a(n) = f(n+1) - f(n).

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