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 A131749 #14 Sep 25 2023 19:26:48
%S A131749 4,2,6,1,3,9,1,2,1,10,0,1,3,4,14,1,1,0,3,1,15,0,1,2,2,5,6,21,1,1,0,2,
%T A131749 0,5,1,22,1,0,1,1,3,3,2,3,25,1,0,0,1,0,3,0,2,1,26,1,0,0,0,1,1,4,4,6,7,
%U A131749 33,1,0,0,0,0,1,0,4,0,6,1,34,0,1,1,1,1,1,2,2,6,6,0,1,35
%N A131749 Triangle of successive absolute differences of semiprimes.
%C A131749 Semiprime analog of A036262. The conjecture analogous to Gilbreath's conjecture is that the leading term (after the second row) is always 0 or 1. First diagonal is semiprimes (A001358). Second diagonal is first differences of semiprimes (A065516).
%H A131749 Robert G. Wilson v, <a href="/A131749/b131749.txt">Table of n, a(n) for n = 1..10011</a>
%H A131749 <a href="/index/Ge#Gilbreath">Index entries for sequences related to Gilbreath conjecture and transform</a>
%e A131749 Table begins:
%e A131749 4 6 9 10 14 15 21 22 25 26 33 34 35 38 39 46 49 51 55 57 58 62 65 69 74 77 82 85
%e A131749 2 3 1 4 1 6 1 3 1 7 1 1 3 1 7 3 2 4 2 1 4 3 4 5 3 5 3
%e A131749 1 2 3 3 5 5 2 2 6 6 0 2 2 6 4 1 2 2 1 3 1 1 1 2 2 2
%e A131749 1 1 0 2 0 3 0 4 0 6 2 0 4 2 3 1 0 1 2 2 0 0 1 0 0
%e A131749 0 1 2 2 3 3 4 4 6 4 2 4 2 1 2 1 1 1 0 2 0 1 1 0
%e A131749 1 1 0 1 0 1 0 2 2 2 2 2 1 1 1 0 0 1 2 2 1 0 1
%e A131749 0 1 1 1 1 1 2 0 0 0 0 1 0 0 1 0 1 1 0 1 1 1
%e A131749 1 0 0 0 0 1 2 0 0 0 1 1 0 1 1 1 0 1 1 0 0
%e A131749 1 0 0 0 1 1 2 0 0 1 0 1 1 0 0 1 1 0 1 0
%e A131749 1 0 0 1 0 1 2 0 1 1 1 0 1 0 1 0 1 1 1
%e A131749 1 0 1 1 1 1 2 1 0 0 1 1 1 1 1 1 0 0
%e A131749 1 1 0 0 0 1 1 1 0 1 0 0 0 0 0 1 0
%e A131749 0 1 0 0 1 0 0 1 1 1 0 0 0 0 1 1
%e A131749 1 1 0 1 1 0 1 0 0 1 0 0 0 1 0
%e A131749 0 1 1 0 1 1 1 0 1 1 0 0 1 1
%e A131749 1 0 1 1 0 0 1 1 0 1 0 1 0
%e A131749 1 1 0 1 0 1 0 1 1 1 1 1
%e A131749 0 1 1 1 1 1 1 0 0 0 0
%e A131749 1 0 0 0 0 0 1 0 0 0
%e A131749 1 0 0 0 0 1 1 0 0
%e A131749 1 0 0 0 1 0 1 0
%e A131749 1 0 0 1 1 1 1
%e A131749 1 0 1 0 0 0
%e A131749 1 1 1 0 0
%e A131749 0 0 1 0
%e A131749 0 1 1
%e A131749 1 0
%e A131749 1
%e A131749 etc.
%t A131749 SemiPrimePi[n_] := Sum[ PrimePi[n/Prime[i]] - i + 1, {i, PrimePi[ Sqrt[n]]}]; SemiPrime[n_] := Block[{e = Floor[Log[2, n] + 1], a, b}, a = 2^e; Do[b = 2^p; While[SemiPrimePi@a < n, a = a + b]; a = a - b/2, {p, e, 0, -1}]; a + b/2]; t[0, n_] := SemiPrime[n]; t[r_, c_] := Abs[t[r - 1, c] - t[r - 1, c + 1]]; Table[t[r - c, c], {r, 13}, {c, r}] // Flatten
%t A131749 (* to construct the table as shown *) mx = 13; Table[t[r, c], {r, 0, mx - 1}, {c, mx - r}] // TableForm (* _Robert G. Wilson v_, Jun 13 2018 *)
%Y A131749 Cf. A001358, A036262, A065516.
%K A131749 easy,nonn,tabl
%O A131749 1,1
%A A131749 _Jonathan Vos Post_, Oct 23 2007