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

1,3

Links

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

Formula

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

Example

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

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

Crossrefs

Cf. A050221, A060863, A082431, A122821.

Sequence in context: A025899 A025869 A093320 * A005136 A138474 A058761

Adjacent sequences: A082367 A082368 A082369 * A082371 A082372 A082373

Keyword

easy,nonn

Author

Naohiro Nomoto, May 11 2003

Extensions

Extended by Ray Chandler, Oct 03 2006

Status

approved