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A105093 Numbers n such that n = prime(k) + prime(k+3) = prime(k+1) + prime(k+2) for some k.

%I A105093 #13 Feb 16 2025 08:32:57
%S A105093 18,24,30,36,60,84,120,162,204,210,216,240,288,330,372,390,456,520,
%T A105093 540,624,726,762,798,840,852,882,924,978,990,1104,1140,1164,1200,1392,
%U A105093 1410,1428,1530,1632,1650,1716,1740,1764,1794,1848,1974,2052,2100,2112,2184
%N A105093 Numbers n such that n = prime(k) + prime(k+3) = prime(k+1) + prime(k+2) for some k.
%H A105093 Chai Wah Wu, <a href="/A105093/b105093.txt">Table of n, a(n) for n = 1..10000</a>
%H A105093 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GoldbachConjecture.html">Goldbach Conjecture</a>
%e A105093 a(1)=18 because prime(3)+prime(6)=prime(4)+prime(5)=5+13=7+11=18.
%t A105093 lst = {}; Do[ If[ Prime[n] + Prime[n + 3] == Prime[n + 1] + Prime[n + 2], AppendTo[lst, Prime[n] + Prime[n + 3]]], {n, 184}]; lst (* _Robert G. Wilson v_, Apr 07 2005 *)
%o A105093 (Python)
%o A105093 from sympy import nextprime
%o A105093 A105093_list, plist = [], [2,3,5,7]
%o A105093 while len(A105093_list) < 10000:
%o A105093     m = plist[0]+plist[3]
%o A105093     if m == plist[1]+plist[2]:
%o A105093         A105093_list.append(m)
%o A105093     plist = plist[1:] + [nextprime(plist[-1])] # _Chai Wah Wu_, Mar 30 2020
%Y A105093 Cf. A001172, A000954, first primes in A022885.
%K A105093 nonn
%O A105093 1,1
%A A105093 _Giovanni Teofilatto_, Apr 06 2005
%E A105093 Edited and extended by _Robert G. Wilson v_, Apr 07 2005