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A366092
Distance from the sum of the first n primes to the nearest prime.
3
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.
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
KEYWORD
nonn,easy
AUTHOR
Paolo Xausa, Sep 29 2023
STATUS
approved