A341827 a(n) is the distance from n to its more distant neighboring prime.

2, 1, 2, 1, 4, 3, 2, 3, 4, 1, 4, 3, 2, 3, 4, 1, 4, 3, 2, 3, 6, 5, 4, 3, 4, 5, 6, 1, 6, 5, 4, 3, 4, 5, 6, 3, 2, 3, 4, 1, 4, 3, 2, 3, 6, 5, 4, 3, 4, 5, 6, 5, 4, 3, 4, 5, 6, 1, 6, 5, 4, 3, 4, 5, 6, 3, 2, 3, 4, 1, 6, 5, 4, 3, 4, 5, 6, 3, 2, 3, 6, 5, 4, 3, 4, 5, 8

Offset: 3

Author

Ya-Ping Lu, Feb 20 2021

Keywords

• nonn

Comments

a(n) is even if n is odd and vice versa. It seems that all records are even.

n - 1 and n + 1 are twin primes if a(n) = 1.

n - 2 and n + 2 are cousin primes for n > 3 if a(n) = 2.

n - 3 and n + 3 are sexy primes if a(n) = A051700(n) = 3.

Crossrefs

Cf. A051700, A051698, A077800, A023200, A046132, A023201, A046117.

Programs

Mathematica

Array[Max[#1 - #2, #3 - #1] & @@ Prepend[NextPrime[#, {-1, 1}], #] &, 105, 3] (* Michael De Vlieger, Mar 17 2021 *)

PARI

for(n=3,88,my(d1=n-precprime(n-1),d2=nextprime(n+1)-n);print1(max(d1,d2),", ")) \\ Hugo Pfoertner, Mar 10 2021

Python

from sympy import prevprime, nextprime
for n in range(3, 1001):
    prevp = prevprime(n); nextp = nextprime(n)
    print(max(n - prevp, nextp - n))

Formula

a(n) = max{n - prevprime(n), nextprime(n) - n}.