A366094 -id:A366094 - cp's OEIS frontend

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

Paolo Xausa, Sep 29 2023

Positions of zeros are given by A013916.

Positions of records are given by A366093.

			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.

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

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

Cf. also A351830, A354330.

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]

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

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

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

A366205 Average of a twin prime pair which is the sum of the first k primes, for some k.

Original entry on oeis.org

6870, 25800, 38238, 125508, 128112, 220512, 372612, 3245688, 4286748, 15433968, 19659138, 23283852, 23494650, 23579262, 26233368, 32131272, 32380728, 34775988, 41299848, 58705260, 61470132, 63588432, 63873960, 91649652, 92774808, 106956252, 124336212, 159723300

Offset: 1

Paolo Xausa, Oct 04 2023

nonn

Paolo Xausa, Table of n, a(n) for n = 1..5000

Intersection of A007504 with A014574.

Cf. A346706, A366094, A366206 (corresponding k values).

With[{upto=10^4},Select[Accumulate[Prime[Range[upto]]],PrimeQ[#-1]&&PrimeQ[#+1]&]]

a(n) = A007504(A366206(n)).

cp's OEIS Frontend

A366092 Distance from the sum of the first n primes to the nearest prime.

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