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 A188268 #24 Feb 01 2019 20:42:15 %S A188268 4,8,153,61,258,649,4134,3384,29295,101468,33607,165325,298594,703923, %T A188268 2393291,32214330,12432950,12849377,539169143,396264119,406027081, %U A188268 33772761,5097974305,4764006510,23719367863,44982489668,54393474823,25708849510 %N A188268 Smallest k such that prime(k) + prime(k+1) = prime(k+2) + prime(k-n). %C A188268 Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics. It states: every even integer greater than 2 can be expressed as the sum of two primes. Because there exist several decompositions (see A002375), this sequence gives k for a second decomposition of prime(k) + prime(k+1) that gives prime(k+2) + prime(k-n). %C A188268 a(n) > pi(2*10^12) for n >= 29. - _Donovan Johnson_, Apr 06 2011 %e A188268 a(2) = 8 because prime(8) + prime(9) = prime(10) + prime(6); i.e., 19 + 23 = 29 + 13. %p A188268 A188268 := proc(n) local k ,pk; k := 1+n ; pk := Array([ithprime(k), ithprime(k+1), ithprime(k+2), ithprime(k-n)]) ; for k from 1+n do if pk[1]+pk[2]-pk[3] = pk[4] then return k ; end if; pk[1] := pk[2] ; pk[2] := pk[3] ; pk[3] := nextprime(pk[2]) ; pk[4] := nextprime(pk[4]) ; end do; end proc: # _R. J. Mathar_, Mar 31 2011 %Y A188268 Cf. A001031, A045917, A002375, A045917. %K A188268 nonn %O A188268 1,1 %A A188268 _Michel Lagneau_, Mar 30 2011 %E A188268 a(23)-a(28) from _Donovan Johnson_, Apr 06 2011