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
Keywords
Examples
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.
Programs
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Mathematica
Select[Range[2, 224, 2], PrimeQ@ Length@ IntegerPartitions[#, {2}, Prime@ Range@ PrimePi@ #] &] (* Giovanni Resta, Dec 06 2019 *) -
Python
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]