A330210 Numbers that can be expressed as the sum of 2 prime numbers in a prime number of different ways.

10, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 38, 40, 44, 48, 52, 54, 56, 62, 64, 68, 70, 74, 76, 78, 82, 86, 94, 96, 98, 104, 112, 124, 128, 130, 136, 140, 144, 148, 156, 158, 164, 168, 174, 176, 178, 186, 188, 192, 194, 198, 206, 208, 210, 216, 218, 222, 224

Offset

1,1

Links

Table of n, a(n) for n=1..58.

Example

24 can be expressed as the sum of 2 prime numbers in 3 different ways (5+19, 7+17, and 11+13), and 3 is prime.

Mathematica

Select[Range[2, 224, 2], PrimeQ@ Length@ IntegerPartitions[#, {2}, Prime@ Range@ PrimePi@ #] &] (* Giovanni Resta, Dec 06 2019 *)

Prog

(Python 3)
import math
from sympy import isprime
def main(n):
    x = {}
    a = 1
    b = 1
    for i in range(2, n):
        x[i] = []
        while a < i:
            if a + b == i:
                x[i].append(str(a) + "+" + str(b))
            b += 1
            if b == i:
                a += 1
                b = 1
        a = 1
        b = 1
    for i in x:
        x[i] = x[i][0:math.ceil(len(x[i])/2)]
    x[2] = ["1+1"]
    newdict = {}
    for i in x:
        newdict[i] = []
        for j in x[i]:
            if isprime(int(j.split("+")[0])) and isprime(int(j.split("+")[1])):
                newdict[i].append(j)
    finaloutput = []
    for i in newdict:
        if isprime(len(newdict[i])):
            finaloutput.append(i)
    return finaloutput
def a(n):
    x = 0
    while len(main(x)) != n:
        x += 1
    return main(x)[-1]

Crossrefs

Cf. A000040, A014091, A061358.

Sequence in context: A088711 A154774 A162708 * A067188 A092632 A213310

Adjacent sequences: A330207 A330208 A330209 * A330211 A330212 A330213

Keyword

nonn

Author

Pietro Saia, Dec 05 2019

Status

approved