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

1,2

Comments

Valus 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

Links

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

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

Formula

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

Maple

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

Mathematica

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

Prog

(PARI)
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

Crossrefs

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

Sequence in context: A351703 A369923 A249094 * A062862 A206799 A084119

Adjacent sequences: A096498 A096499 A096500 * A096502 A096503 A096504

Keyword

nonn

Author

Labos Elemer, Jul 09 2004

Status

approved