This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A080854 #19 Jul 14 2025 16:03:13
%S A080854 48,54,64,70,76,104,106,118,124,134,136,146,148,164,166,188
%N A080854 Numbers which can be expressed as the sum of two distinct primes in exactly five ways.
%C A080854 Apparently there are no further terms beyond 188. - _R. J. Mathar_, Oct 01 2021
%F A080854 {j: A117929(j) = 5} . - _R. J. Mathar_, Oct 01 2021
%e A080854 54 is a term as 54 = 31 + 23 = 37 + 17 = 41 + 13 = 43 + 11 = 47 + 7 are only the five ways to express 54 as a sum of two distinct primes.
%t A080854 Select[Range[200],Count[IntegerPartitions[#,{2}],_?(AllTrue[#,PrimeQ]&&#[[1]]!=#[[2]]&)]==5&] (* _Harvey P. Dale_, Jul 14 2025 *)
%Y A080854 Cf. A077914 (2 ways), A077969 (3 ways), A078299 (4 ways), A080862 (6 ways).
%K A080854 nonn
%O A080854 1,1
%A A080854 _Shyam Sunder Gupta_, Mar 29 2003