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%I #18 Mar 30 2020 19:49:59
%S 24,30,60,84,102,210,234,288,330,378,420,426,496,528,588,594,624,690,
%T 1050,1156,1200,1218,1302,1336,1410,1470,1484,1638,1650,1680,1686,
%U 1716,1734,1740,1746,1788,1848,1908,1918,1930,2052,2154,2226,2364,2410,2580,2892,2934,3168,3524,4080
%N Numbers m such that m = prime(k) + prime(k+5) = prime(k+1) + prime(k+4) for some k.
%C Terms are always even because all primes used in this sequence are odd.
%C Conjecture: this sequence is infinite.
%e a(1)=24 because prime(3)+prime(8)=prime(4)+prime(7)=5+19=7+17.
%t (#[[1]] + #[[6]]) & /@ Select[ Partition[ Prime@ Range@ 320, 6, 1], #[[1]] + #[[6]] == #[[2]] + #[[5]] &] (* _Giovanni Resta_, Mar 08 2020 *)
%o (Python)
%o from sympy import nextprime
%o A333122_list, plist = [], [2,3,5,7,11,13]
%o while len(A333122_list) < 10000:
%o m = plist[0]+plist[5]
%o if m == plist[1]+plist[4]:
%o A333122_list.append(m)
%o plist = plist[1:] + [nextprime(plist[-1])] # _Chai Wah Wu_, Mar 30 2020
%Y Cf. A022889 (the prime(k) primes), A105093 (similar sequence).
%K nonn
%O 1,1
%A _Marcin Barylski_, Mar 08 2020
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