A050237 -id:A050237 - cp's OEIS frontend

A346399 a(n) is the number of symmetrically distributed consecutive primes centered at n (including n itself if n is prime).

0, 1, 1, 2, 3, 2, 1, 0, 4, 0, 1, 6, 1, 0, 6, 0, 1, 4, 1, 0, 2, 0, 1, 0, 0, 2, 0, 0, 1, 10, 1, 0, 0, 2, 0, 0, 1, 0, 2, 0, 1, 6, 1, 0, 2, 0, 1, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 1, 4, 1, 0, 0, 2, 0, 0, 1, 0, 2, 0, 1, 2, 1, 0, 0, 2, 0, 0, 1, 0, 4, 0, 1, 0, 0, 2, 0

Offset: 1

Ya-Ping Lu, Sep 18 2021

nonn

a(n) is the number of consecutive primes in Goldbach pairs of 2n centered at n.
a(n) is odd if n is prime; otherwise, a(n) is even.
n is prime if a(n) = 1 and n is composite if a(n) = 0.
a(n) = 14 is not seen until n = 8021811 (with none higher through 4*10^7). - Bill McEachen, Jul 26 2024

			a(1) = 0 because no prime is <= 1.
a(2) = 1 because no prime is < 2 and {2} is the only symmetrically distributed prime centered at 2.
a(30) = 10 because there are 10 symmetrically distributed consecutive primes, {13, 17, 19, 23, 29, 31, 37, 41, 43, 47}, centered at 30.

Jason Yuen, Table of n, a(n) for n = 1..10000

Cf. A045917, A050237, A060863, A122821.

from sympy import isprime
for n in range(1, 100):
    d = 1 if n%2 == 0 else 2
    ct = 1 if isprime(n) else 0
    while n - d > 2:
        k = isprime(n+d) + isprime(n-d)
        if k == 2: ct += 2
        elif k == 1: break
        d += 2
    print(ct)

A122821 Number of ways n can be represented as the arithmetic mean of consecutive primes.

Original entry on oeis.org

0, 1, 1, 1, 2, 1, 1, 0, 2, 0, 1, 3, 1, 0, 3, 0, 2, 2, 1, 0, 1, 2, 2, 0, 0, 2, 0, 0, 2, 5, 2, 0, 0, 3, 0, 0, 2, 4, 2, 0, 1, 3, 2, 0, 1, 1, 2, 0, 2, 1, 5, 1, 4, 0, 2, 2, 0, 0, 1, 3, 1, 0, 0, 2, 0, 0, 1, 1, 4, 1, 2, 1, 1, 0, 0, 1, 1, 3, 2, 0, 2, 2, 1, 0, 0, 1, 5, 0, 3, 0, 1, 1, 1, 0, 2, 2, 2, 0, 1, 1, 3, 3, 1, 0, 4

Offset: 1

Ray Chandler, Sep 28 2006

nonn

Cf. A050221, A050237, A060863, A060864, A082370.

f[n_]:=Block[{i=1,j,c=0,m},While[Prime[i]<=n, j=1; While[m=Sum[Prime[k],{k,i,i+j-1}]/j; If[m==n,c++ ]; m

A082431 a(n) = the smallest prime p such that there are exactly n sets of consecutive primes, each of which has an arithmetic mean of p.

Original entry on oeis.org

2, 5, 89, 53, 157, 173, 1597, 15233, 8803, 106753, 1570927, 5296771

Offset: 1

Naohiro Nomoto, May 11 2003

			a(4) = 53 because there are exactly four sets of consecutive primes which have means of 53: {53}, {47,53,59}, {41,...,67} and {31,...,73},

Cf. A050221, A050237, A060863, A082370.

{a(n)= m=2; starting_index=1; k=starting_index; sum_of_primes=0; prime_count=0; sets=0; until( (prime(starting_index)>m) && (sets==n), if( (prime(starting_index)>m) || (sets>n), m=nextprime(m+1); sets=0; starting_index=1; k=starting_index); sum_of_primes=sum_of_primes+prime(k); prime_count++; mean=sum_of_primes/prime_count; if(meanRick L. Shepherd, Jun 14 2004

Edited by Don Reble, Jun 17 2003

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A346399 a(n) is the number of symmetrically distributed consecutive primes centered at n (including n itself if n is prime).

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A122821 Number of ways n can be represented as the arithmetic mean of consecutive primes.

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A082431 a(n) = the smallest prime p such that there are exactly n sets of consecutive primes, each of which has an arithmetic mean of p.

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