A071704 Number of ways to represent the n-th prime as arithmetic mean of three other odd primes.

0, 0, 0, 2, 5, 7, 10, 14, 16, 24, 29, 31, 42, 40, 43, 52, 62, 70, 75, 87, 82, 96, 102, 112, 127, 137, 136, 142, 154, 154, 186, 199, 204, 215, 233, 248, 250, 262, 272, 284, 309, 324, 344, 334, 348, 358, 406, 414, 430, 446, 441, 489, 486, 511, 508

Offset

1,4

Links

Robert Israel, Table of n, a(n) for n = 1..2000

Example

a(5)=5 as A000040(5)=11 and there are no more representations not containing 11 than 11 = (3+7+23)/3 = (3+13+17)/3 = (5+5+23)/3 = (7+7+19)/3 = (7+13+13)/3.

Maple

N:= 300: # to get the first A000720(N) terms
P:= select(isprime, [seq(i, i=3..3*N, 2)]):
nP:= nops(P):
V:= Vector(N):
for i from 1 to nP do
  for j from i to nP do
    for k from j to nP while P[i]+P[j]+P[k] <= 3*N do
      r:= (P[i]+P[j]+P[k])/3;
      if r::integer and isprime(r) and r <> P[j] and r <= N then V[r]:= V[r]+1 fi
od od od:
seq(V[ithprime(i)], i=1..numtheory:-pi(N)); # Robert Israel, Aug 09 2018

Mathematica

M = 300; (* to get the first A000720(M) *)
P = Select[Range[3, 3*M, 2], PrimeQ]; nP = Length[P]; V = Table[0, {M}];
For[i = 1, i <= nP, i++,
For[j = i, j <= nP, j++,
For[k = j, k <= nP && P[[i]] + P[[j]] + P[[k]] <= 3*M , k++, r = (P[[i]] + P[[j]] + P[[k]])/3; If[IntegerQ[r] && PrimeQ[r] && r != P[[j]] && r <= M, V[[r]] = V[[r]]+1]
]]];
Table[V[[Prime[i]]], {i, 1, PrimePi[M]}] (* Jean-François Alcover, Mar 09 2019, after Robert Israel *)

Prog

(Haskell)
a071704 n = z (us ++ vs) 0 (3 * q)  where
   z _ 3 m = fromEnum (m == 0)
   z ps'@(p:ps) i m = if m < p then 0 else z ps' (i+1) (m - p) + z ps i m
   (us, _:vs) = span (< q) a065091_list; q = a000040 n
-- Reinhard Zumkeller, May 24 2015
(PARI) a(n, p=prime(n))=my(s=0); forprime(q=p+2, 3*p-4, my(t=3*p-q); forprime(r=max(t-q, 3), (3*p-q)\2, if(t!=p+r && isprime(t-r), s++))); s \\ Charles R Greathouse IV, Jun 04 2015

Crossrefs

Cf. A071681, A071703, A000040, A065091, A258233.

Sequence in context: A088947 A288209 A071113 * A267374 A267379 A287403

Adjacent sequences: A071701 A071702 A071703 * A071705 A071706 A071707

Keyword

nonn

Author

Reinhard Zumkeller, Jun 03 2002

Extensions

Definition corrected by Zak Seidov, May 24 2015

Status

approved