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 A330210 Numbers that can be expressed as the sum of 2 prime numbers in a prime number of different ways. 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS 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

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Last modified July 27 02:39 EDT 2021. Contains 346302 sequences. (Running on oeis4.)