cp's OEIS Frontend

A333122 Numbers m such that m = prime(k) + prime(k+5) = prime(k+1) + prime(k+4) for some k.

%I A333122 #18 Mar 30 2020 19:49:59
%S A333122 24,30,60,84,102,210,234,288,330,378,420,426,496,528,588,594,624,690,
%T A333122 1050,1156,1200,1218,1302,1336,1410,1470,1484,1638,1650,1680,1686,
%U A333122 1716,1734,1740,1746,1788,1848,1908,1918,1930,2052,2154,2226,2364,2410,2580,2892,2934,3168,3524,4080
%N A333122 Numbers m such that m = prime(k) + prime(k+5) = prime(k+1) + prime(k+4) for some k.
%C A333122 Terms are always even because all primes used in this sequence are odd.
%C A333122 Conjecture: this sequence is infinite.
%e A333122 a(1)=24 because prime(3)+prime(8)=prime(4)+prime(7)=5+19=7+17.
%t A333122 (#[[1]] + #[[6]]) & /@ Select[ Partition[ Prime@ Range@ 320, 6, 1], #[[1]] + #[[6]] == #[[2]] + #[[5]] &] (* _Giovanni Resta_, Mar 08 2020 *)
%o A333122 (Python)
%o A333122 from sympy import nextprime
%o A333122 A333122_list, plist = [], [2,3,5,7,11,13]
%o A333122 while len(A333122_list) < 10000:
%o A333122     m = plist[0]+plist[5]
%o A333122     if m == plist[1]+plist[4]:
%o A333122         A333122_list.append(m)
%o A333122     plist = plist[1:] + [nextprime(plist[-1])] # _Chai Wah Wu_, Mar 30 2020
%Y A333122 Cf. A022889 (the prime(k) primes), A105093 (similar sequence).
%K A333122 nonn
%O A333122 1,1
%A A333122 _Marcin Barylski_, Mar 08 2020