A080378 Residues mod 4 of the n-th difference between consecutive primes.

1, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2

Offset: 1

Author

Labos Elemer, Mar 04 2003

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Sequences related to the differences between successive primes: A001223 (Delta(p)), A028334, A080378, A104120, A330556-A330561.

Programs

Mathematica

Table[Mod[Prime[w+1]-Prime[w], 4], {w, 1, 256}]
Mod[Differences[Prime[Range[200]]], 4] (* Zak Seidov, Jun 26 2015 *)

Python

from sympy import prime
def A080378(n): return (prime(n+1)-prime(n))&3 # Chai Wah Wu, Jul 07 2022

Formula

a(n) = A001223(n) mod 4.