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%I #22 Oct 03 2023 10:34:13
%S 2,2,5,11,17,29,41,59,79,101,127,157,197,239,281,331,379,439,499,569,
%T 641,709,787,877,967,1061,1163,1259,1373,1481,1597,1721,1847,1987,
%U 2129,2273,2423,2579,2749,2917,3089,3271,3449,3637,3833,4027,4229,4441,4663,4889
%N Least prime nearest to the sum of the first n primes.
%H Paolo Xausa, <a href="/A366094/b366094.txt">Table of n, a(n) for n = 0..10000</a>
%e a(3) = 11 because the sum of the first 3 primes is 2 + 3 + 5 = 10 and the nearest prime is 11.
%e a(10) = 127 because the sum of the first 10 primes is 129, which is equidistant from the nearest primes (127 and 131), and 127 is the smaller one.
%t pNearest[n_]:=If[PrimeQ[n],n,With[{np=NextPrime[n],pp=NextPrime[n,-1]},If[np-n<n-pp,np,pp]]];
%t A366094list[nmax_]:=Prepend[Map[pNearest,Accumulate[Prime[Range[nmax]]]],2];
%t A366094list[100]
%o (Python)
%o from sympy import prime, nextprime, prevprime
%o def A366094(n): return (p if ((m:=sum(prime(i) for i in range(1,n+1)))<<1)-(p:=prevprime(m+1))<=(k:=nextprime(m)) else k) if n else 2 # _Chai Wah Wu_, Oct 03 2023
%Y Cf. A000040, A007504, A366092.
%Y Cf. A353295, A354329.
%K nonn,easy
%O 0,1
%A _Paolo Xausa_, Sep 29 2023