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 A180565 #24 Jun 13 2017 03:51:16
%S A180565 5,9,17,29,77,197,689,44537,159617,374249,695957,4343237,8439595349,
%T A180565 196119836669,45036059849537,108841069412237,505069584287297
%N A180565 Numbers starting with 5 such that the sum of any two distinct entries is two times some prime.
%C A180565 The numbers starting with 1 are in the set {1, 5, 9} because if another number q = 2k + 1 exists, then k+1, k+3 and k+5 are primes only if k = 2, but q=5 is already in the set.
%C A180565 The numbers starting with 3 are given by A115760.
%C A180565 The numbers starting with 7 are 7, 15, 19, 67, 127, 187, 547, 607, ...
%F A180565 a(n) = 2*A093483(n)+1 (follows from the definition). - _Chris Boyd_, Mar 16 2014
%e A180565 For the set of the first three entries, 5+9 = 2*7, 5+17 = 2*11, 9+17 = 2*13.
%p A180565 A180565 := proc(n) option remember; if n = 1 then 5; else for a from procname(n-1)+1 do wrks := true ; for prev from 1 to n-1 do if not type((procname(prev)+a)/2,prime) then wrks := false; break; end if; end do: if wrks then return a; end if; end do: end if; end proc: # _R. J. Mathar_, Jan 24 2011
%Y A180565 Cf. A115760.
%K A180565 nonn,more
%O A180565 1,1
%A A180565 _Michel Lagneau_, Jan 21 2011
%E A180565 a(14)-a(17) from _Chris Boyd_, Mar 16 2014