A366092 -id:A366092 - cp's OEIS frontend

A366093 Indices of records in A366092.

0, 11, 22, 27, 58, 61, 110, 126, 161, 545, 566, 592, 747, 775, 2286, 5343, 5360, 5741, 18245, 78272, 93999, 140690, 146338, 227734, 251721, 274297, 372294, 447238, 586777, 808500, 7185887, 10479806, 37485090, 85742340, 91332097, 111764212, 117522098, 556747657, 589122990

Offset: 1

Paolo Xausa, Sep 29 2023

Cf. A366092.

pDist[n_]:=If[PrimeQ[n],0,Min[NextPrime[n]-n,n-NextPrime[n,-1]]];
A366093list[upto_]:=Module[{r=-1,a={},d=Map[pDist,Prepend[Accumulate[Prime[Range[upto]]],0]]},Do[If[d[[i]]>r,r=d[[i]];AppendTo[a,i-1]],{i,upto}];a];
A366093list[10000]

from itertools import count, islice
from sympy import prevprime, nextprime
def A366093_gen(): # generator of terms
    c, s, p = 2, 0, 1
    yield 0
    for i in count(1):
        if (m:=min((s:=s+(p:=nextprime(p)))-prevprime(s+1),nextprime(s)-s))>c:
            yield i
            c = m
A366093_list = list(islice(A366093_gen(),20)) # Chai Wah Wu, Oct 03 2023

a(31)-a(39) from Michael S. Branicky, Oct 03 2023

A366094 Least prime nearest to the sum of the first n primes.

Original entry on oeis.org

2, 2, 5, 11, 17, 29, 41, 59, 79, 101, 127, 157, 197, 239, 281, 331, 379, 439, 499, 569, 641, 709, 787, 877, 967, 1061, 1163, 1259, 1373, 1481, 1597, 1721, 1847, 1987, 2129, 2273, 2423, 2579, 2749, 2917, 3089, 3271, 3449, 3637, 3833, 4027, 4229, 4441, 4663, 4889

Offset: 0

Paolo Xausa, Sep 29 2023

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

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

Cf. A000040, A007504, A366092.

Cf. A353295, A354329.

pNearest[n_]:=If[PrimeQ[n],n,With[{np=NextPrime[n],pp=NextPrime[n,-1]},If[np-nA366094list[nmax_]:=Prepend[Map[pNearest,Accumulate[Prime[Range[nmax]]]],2];
A366094list[100]

from sympy import prime, nextprime, prevprime
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

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A366093 Indices of records in A366092.

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