A082370 a(n) = number of sets of consecutive primes whose arithmetic mean is A000040(n).

1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 2, 2, 1, 2, 2, 4, 1, 1, 1, 2, 1, 2, 1, 3, 2, 3, 1, 2, 1, 3, 3, 1, 2, 4, 3, 3, 5, 1, 1, 6, 2, 3, 1, 2, 1, 2, 3, 2, 3, 2, 1, 1, 2, 2, 2, 4, 2, 1, 2, 4, 3, 3, 3, 2, 2, 1, 2, 1, 4, 3, 5, 2, 1, 2, 1, 3, 1, 3, 1, 3, 3, 2, 3, 2, 3, 1, 1, 2, 1, 5, 2, 1, 2, 3, 1, 2, 1, 3, 3, 2, 1, 1, 5, 2, 2

Offset: 1

Author

Naohiro Nomoto, May 11 2003

Keywords

• easy
• nonn

Examples

			For n=3; A000040(3) = 5. the two sets are 5/1 = 5, (3+5+7)/3 = 5. so a(3)=2.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..4000

Crossrefs

Cf. A050221, A060863, A082431, A122821.

Programs

Maple

N:= 300:
P:= [0,seq(ithprime(i),i=1..N)]:
S:= ListTools:-PartialSums(P):
mmax:= numtheory:-pi(floor(S[N]/N)):
V:= Vector(1..mmax,1):
for i from 1 to N+1 do
  for j from i+2 to N+1 do
    r:= (S[j]-S[i])/(j-i);
    if r::integer and isprime(r) then
      k:= numtheory:-pi(r);
      if k <= mmax then
        V[k]:= V[k]+1
      fi
    fi
od od:
convert(V,list); # Robert Israel, Mar 18 2018

Formula

a(n) = A122821(A000040(n)).

Extensions

Extended by Ray Chandler, Oct 03 2006