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

%I A082370 #9 Mar 18 2018 04:30:25
%S A082370 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,
%T A082370 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,
%U A082370 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
%N A082370 a(n) = number of sets of consecutive primes whose arithmetic mean is A000040(n).
%H A082370 Robert Israel, <a href="/A082370/b082370.txt">Table of n, a(n) for n = 1..4000</a>
%F A082370 a(n) = A122821(A000040(n)).
%e A082370 For n=3; A000040(3) = 5. the two sets are 5/1 = 5, (3+5+7)/3 = 5. so a(3)=2.
%p A082370 N:= 300:
%p A082370 P:= [0,seq(ithprime(i),i=1..N)]:
%p A082370 S:= ListTools:-PartialSums(P):
%p A082370 mmax:= numtheory:-pi(floor(S[N]/N)):
%p A082370 V:= Vector(1..mmax,1):
%p A082370 for i from 1 to N+1 do
%p A082370   for j from i+2 to N+1 do
%p A082370     r:= (S[j]-S[i])/(j-i);
%p A082370     if r::integer and isprime(r) then
%p A082370       k:= numtheory:-pi(r);
%p A082370       if k <= mmax then
%p A082370         V[k]:= V[k]+1
%p A082370       fi
%p A082370     fi
%p A082370 od od:
%p A082370 convert(V,list); # _Robert Israel_, Mar 18 2018
%Y A082370 Cf. A050221, A060863, A082431, A122821.
%K A082370 easy,nonn
%O A082370 1,3
%A A082370 _Naohiro Nomoto_, May 11 2003
%E A082370 Extended by _Ray Chandler_, Oct 03 2006