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 A066722 #21 Apr 22 2025 14:07:20
%S A066722 60,66,72,100,106,110,116,118,134,146,166,172,182,212,248,332
%N A066722 Numbers that can be expressed as the sum of two primes in exactly six ways.
%C A066722 No other terms below 10000. I conjecture there are no further terms in this sequence and A067188, A067189, etc.
%C A066722 _R. K. Guy_ (Jan 14 2002) remarks: "I believe that these conjectures follow from a more general one by Hardy and Littlewood (probably in Some problems of 'partitio numerorum' III, on the expression of a number as a sum of primes, Acta Math. 44(1922) 1-70)."
%H A066722 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%t A066722 y = Select[Flatten@Table[Prime[i] + Prime[ j], {i, 500}, {j, 1, i}], # < Prime[500] &]; Select[Union[y], Count[y, #] == 6 &] (* _Robert Price_, Apr 22 2025 *)
%Y A066722 Numbers that can be expressed as the sum of two primes in k ways for k=0..10: A014092 (k=0), A067187 (k=1), A067188 (k=2), A067189 (k=3), A067190 (k=4), A067191 (k=5), this sequence (k=6), A352229 (k=7), A352230 (k=8), A352231 (k=9), A352233 (k=10).
%K A066722 nonn
%O A066722 1,1
%A A066722 Peter Bertok (peter(AT)bertok.com), Jan 13 2002