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 A154727 #17 Feb 16 2025 08:33:09
%S A154727 1,2,3,3,5,3,7,5,7,3,11,3,5,11,13,5,7,11,13,3,7,13,17,3,5,17,19,5,7,
%T A154727 11,13,17,19,3,7,19,23,5,11,17,23,7,11,13,17,19,23,3,13,19,29,3,5,11,
%U A154727 23,29,31,5,7,13,17,19,23,29,31,7,31,3,11,17
%N A154727 Triangle read by rows in which row n lists all the pairs of prime numbers that are equidistant from n, or only n if there is no such pair, as shown below in the example.
%C A154727 If the extended Goldbach conjecture is true, such a pair exists in row n for all n >= 4. - _Nathaniel Johnston_, Apr 18 2011
%H A154727 Nathaniel Johnston, <a href="/A154727/b154727.txt">Table of n, a(n) for n = 1..10000</a>
%H A154727 Wolfram MathWorld, <a href="https://mathworld.wolfram.com/GoldbachConjecture.html">Goldbach Conjecture</a>
%e A154727 Triangle begins:
%e A154727 1
%e A154727 2
%e A154727 3
%e A154727 3, . 5
%e A154727 3, . . . 7
%e A154727 . . 5, . 7, . .
%e A154727 3, . . . . . . . 11
%e A154727 3, . 5, . . . . . 11, . 13
%e A154727 . . 5, . 7, . . . 11, . 13, . .
%e A154727 3, . . . 7, . . . . . 13, . . . 17
%p A154727 print(1):print(2):print(3):for n from 1 to 15 do for k from 1 to 2*n-1 do if(not k=n and (isprime(k) and isprime(2*n-k)))then print(k):fi:od:od: # _Nathaniel Johnston_, Apr 18 2011
%t A154727 Table[n + Union@ Join[#, -#] /. {} -> {n} &@ Select[DeleteCases[n - Prime@ Range[2, PrimePi@ n], 0], AllTrue[n + # {-1, 1}, PrimeQ] &], {n, 20}] // Flatten (* _Michael De Vlieger_, Feb 03 2019 *)
%Y A154727 Cf. A000040, A154720, A154721, A154722, A154723, A154724, A154725, A154726.
%K A154727 easy,nonn,tabf
%O A154727 1,2
%A A154727 _Omar E. Pol_, Jan 14 2009, Jan 16 2009
%E A154727 a(24)-a(70) from _Nathaniel Johnston_, Apr 18 2011