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 A319494 #22 Nov 15 2018 15:12:23
%S A319494 2,1,3,1,2,1,5,0,1,2,2,1,7,2,2,1,4,0,2,1,11,2,0,2,1,2,0,0,2,1,13,2,0,
%T A319494 0,2,1,4,0,0,0,0,1,17,2,0,0,2,0,1,2,0,0,2,0,0,1,19,2,0,2,2,0,0,1,4,0,
%U A319494 2,0,0,0,0,1
%N A319494 Triangle of the consecutive absolute differences between consecutive elements of the previous row, first row being the prime numbers (A000040), read by columns.
%C A319494 Gilbreath's conjecture says that the first element of each row except the first row equals 1. - _Rémy Sigrist_, Nov 15 2018
%H A319494 Wikipedia, <a href="https://en.wikipedia.org/wiki/Gilbreath's_conjecture">Gilbreath's conjecture</a>
%e A319494 1st column
%e A319494 | 2nd column
%e A319494 | | 3rd column
%e A319494 | | | 4th column
%e A319494 v | v | ...
%e A319494 v v
%e A319494 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 ...
%e A319494 1 2 2 4 2 4 2 4 6 2 6 4 2 4 ...
%e A319494 1 0 2 2 2 2 2 2 4 4 2 2 2 ...
%e A319494 1 2 0 0 0 0 0 2 0 2 0 0 ... .
%e A319494 1 2 0 0 0 0 2 2 2 2 0 ... .
%e A319494 1 2 0 0 0 2 0 0 0 2 ... .
%e A319494 1 2 0 0 2 2 0 0 2 ... .
%e A319494 1 2 0 2 0 2 0 2 ... .
%e A319494 1 2 2 2 2 2 2 ... .
%e A319494 1 0 0 0 0 0 ... .
%e A319494 1 0 0 0 0 ... .
%e A319494 1 0 0 0 ... .
%e A319494 1 0 0 ... .
%e A319494 1 0 ... .
%e A319494 1 ... .
%o A319494 (PARI) T(n, k) = {if (k==n, return (prime(n))); abs(T(n, k+1) - T(n-1, k));}
%o A319494 tabl(nn) = for (n=1, nn, for (k=1, n, print1(T(n,k), ", ")); print); \\ _Michel Marcus_, Oct 28 2018
%Y A319494 First row consists of the prime numbers (A000040).
%Y A319494 Second row gives the absolute values of differences between consecutive primes (A001223).
%Y A319494 Third row gives the absolute values of second differences between primes (A036263 in absolute value).
%Y A319494 Fourth row gives the absolute values of differences of absolute values of second differences between primes (A036272).
%Y A319494 ...
%Y A319494 Cf. A036261.
%K A319494 nonn,tabl
%O A319494 1,1
%A A319494 _Tristan Cam_, Sep 20 2018