A366092 Distance from the sum of the first n primes to the nearest prime.

2, 0, 0, 1, 0, 1, 0, 1, 2, 1, 2, 3, 0, 1, 0, 3, 2, 1, 2, 1, 2, 3, 4, 3, 4, 1, 2, 5, 2, 1, 4, 1, 4, 1, 2, 3, 4, 5, 2, 3, 2, 5, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 10, 1, 0, 11, 2, 1, 0, 3, 2, 3, 2, 7, 2, 1, 2, 3, 4, 3, 2, 3, 4, 5, 2, 5, 4, 3, 10, 3

Offset: 0

Author

Paolo Xausa, Sep 29 2023

Keywords

• nonn
• easy

Comments

Positions of zeros are given by A013916.

Positions of records are given by A366093.

Examples

			a(3) = 1 because the sum of the first 3 primes is 2 + 3 + 5 = 10, the nearest prime is 11 and 11 - 10 = 1.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000040, A007504, A013916, A051699, A366093, A366094.

Cf. also A351830, A354330.

Programs

Mathematica

pDist[n_]:=If[PrimeQ[n],0,Min[NextPrime[n]-n,n-NextPrime[n,-1]]];
A366092list[nmax_]:=Map[pDist,Prepend[Accumulate[Prime[Range[nmax]]],0]];
A366092list[100]

Python

from sympy import prime, nextprime, prevprime
def A366092(n): return min((m:=sum(prime(i) for i in range(1,n+1)))-prevprime(m+1),nextprime(m)-m) if n else 2 # Chai Wah Wu, Oct 03 2023

Formula

a(n) = A051699(A007504(n)).

a(n) = abs(A007504(n) - A366094(n)).