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

1,2

Links

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A050314 A316344 A122157 * A243865 A120439 A248512

Adjacent sequences: A080375 A080376 A080377 * A080379 A080380 A080381

Keyword

nonn

Author

Labos Elemer, Mar 04 2003

Status

approved