A082370 -id:A082370 - cp's OEIS frontend

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

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

cp's OEIS Frontend

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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