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

0,1

Comments

Positions of zeros are given by A013916.

Positions of records are given by A366093.

Links

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

Formula

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

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

Example

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.

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]

Prog

(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

Crossrefs

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

Cf. also A351830, A354330.

Sequence in context: A345375 A101669 A243067 * A086965 A256572 A025463

Adjacent sequences: A366089 A366090 A366091 * A366093 A366094 A366095

Keyword

nonn,easy

Author

Paolo Xausa, Sep 29 2023

Status

approved