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A339485 Number of subsets of the first n primes whose elements have a prime average. 2
1, 2, 3, 6, 9, 12, 17, 30, 51, 88, 149, 264, 439, 746, 1261, 2234, 4211, 7996, 14899, 28048, 54037, 106442, 208625, 398588, 735365, 1331590, 2421573, 4481896, 8504953, 16497150, 32595915, 64614636, 127968263, 252470776, 495388085, 962475122, 1847742473, 3504948056 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..150

Eric W. Weisstein's World of Mathematics, Arithmetic Mean

EXAMPLE

a(5) = 9 subsets: {2}, {3}, {5}, {7}, {11}, {3, 7}, {3, 11}, {3, 5, 7} and {3, 7, 11}.

MAPLE

b:= proc(n, s, c) option remember; `if`(n=0,

      `if`(c>0 and denom(s)=1 and isprime(s), 1, 0),

       b(n-1, s, c)+b(n-1, (s*c+ithprime(n))/(c+1), c+1))

    end:

a:= n-> b(n, 0$2):

seq(a(n), n=1..40);  # Alois P. Heinz, Dec 08 2020

MATHEMATICA

b[n_, s_, c_] := b[n, s, c] = If[n == 0,

     If[c > 0 && Denominator[s] == 1 && PrimeQ[s], 1, 0],

     b[n-1, s, c] + b[n-1, (s*c + Prime[n])/(c+1), c+1]];

a[n_] := b[n, 0, 0];

Array[a, 40] (* Jean-Fran├žois Alcover, Jul 09 2021, after Alois P. Heinz *)

PROG

(Python)

from sympy import prime, isprime

from itertools import chain, combinations

def powerset(s): # skip empty set and singletons

    return chain.from_iterable(combinations(s, r) for r in range(2, len(s)+1))

def a(n):

    out = n  # count all singletons

    for s in powerset([prime(i) for i in range(1, n+1)]):

        ss = sum(s)

        if ss%len(s) == 0:

            if isprime(ss//len(s)): out += 1

    return out

print([a(n) for n in range(1, 21)]) # Michael S. Branicky, Dec 06 2020

(Python)

from itertools import combinations

from sympy import prime

def A339485(n):

    c, primeset2 = n, set(prime(i) for i in range(1, n))

    primeset = primeset2 | {prime(n)}

    for l in range(2, n+1):

        for d in combinations(primeset, l):

            a, b = divmod(sum(d), l)

            if b == 0 and a in primeset2:

                c += 1

    return c # Chai Wah Wu, Dec 07 2020

CROSSREFS

Cf. A000040, A051293, A071810, A127542, A309160.

Sequence in context: A213172 A008810 A280984 * A176893 A144677 A309677

Adjacent sequences:  A339482 A339483 A339484 * A339486 A339487 A339488

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 06 2020

EXTENSIONS

a(10)-a(30) from Michael S. Branicky, Dec 06 2020

a(31)-a(34) from Chai Wah Wu, Dec 07 2020

a(35)-a(36) from Michael S. Branicky, Dec 08 2020

a(37)-a(38) from Chai Wah Wu, Dec 08 2020

STATUS

approved

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Last modified July 24 14:12 EDT 2021. Contains 346273 sequences. (Running on oeis4.)