A366092 - OEIS

%I #20 Oct 03 2023 10:33:52

%S 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,

%T 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,

%U 3,2,7,2,1,2,3,4,3,2,3,4,5,2,5,4,3,10,3

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

%C Positions of zeros are given by A013916.

%C Positions of records are given by A366093.

%H Paolo Xausa, <a href="/A366092/b366092.txt">Table of n, a(n) for n = 0..10000</a>

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

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

%e 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.

%t pDist[n_]:=If[PrimeQ[n],0,Min[NextPrime[n]-n,n-NextPrime[n,-1]]];

%t A366092list[nmax_]:=Map[pDist,Prepend[Accumulate[Prime[Range[nmax]]],0]];

%t A366092list[100]

%o (Python)

%o from sympy import prime, nextprime, prevprime

%o 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

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

%Y Cf. also A351830, A354330.

%K nonn,easy

%O 0,1

%A _Paolo Xausa_, Sep 29 2023