A096500 -id:A096500 - cp's OEIS frontend

A096501 Difference between primes preceding n+1 and n.

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

Offset: 1

Labos Elemer, Jul 09 2004

nonn

Values a(1) = 0 and a(2) = 4 are based on convention in Mathematica-language that PreviousPrime(1) = PreviousPrime(2) = -2. - Antti Karttunen, Jan 03 2019

Antti Karttunen, Table of n, a(n) for n = 1..20000
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Cf. A000720, A001223, A010051, A096500, A136548, A151799, A175851, A007917.

0,4,seq(prevprime(n+1)-prevprime(n),n=3..150); # Muniru A Asiru, Jan 03 2019

Table[NextPrime[n+1, -1] - NextPrime[n, -1], {n, 1, 256}]
Differences[NextPrime[Range[110],-1]] (* Harvey P. Dale, Jul 09 2017 *)

A136548(n) = if(n<3,1,precprime(n-1));
A096501(n) = if(2==n,4,A136548(1+n)-A136548(n)); \\ Antti Karttunen, Jan 03 2019

For n > 2, a(n) = A010051(n) * A001223(A000720(n)-1) = A136548(1+n)-A136548(n). - Antti Karttunen, Jan 03 2019

a(n) = A007917(n) - A007917(n-1), for n > 2. - Ridouane Oudra, Oct 05 2024

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

A096501 Difference between primes preceding n+1 and n.

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