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

3,1

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.

Links

Table of n, a(n) for n=3..89.

Formula

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A159272 A098372 A177236 * A138567 A103530 A090924

Adjacent sequences: A341824 A341825 A341826 * A341828 A341829 A341830

Keyword

nonn

Author

Ya-Ping Lu, Feb 20 2021

Status

approved