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A071704 Number of ways to represent the n-th prime as arithmetic mean of three other odd primes. 4
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified October 17 02:04 EDT 2019. Contains 328106 sequences. (Running on oeis4.)