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 A174433 #9 Jun 28 2024 21:10:41 %S A174433 0,0,1,0,1,1,0,1,1,3,0,1,1,3,1,0,1,1,1,1,1,0,1,1,1,1,1,1,0,1,1,3,1,3, %T A174433 1,3,0,1,1,3,1,3,1,3,5,0,1,1,1,1,1,1,1,5,1,0,1,1,3,1,3,1,3,1,1,1,0,1, %U A174433 1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,5,1,5,1,1,0,1,1,3,1,3,1,3,1,1,1,3,1,3 %N A174433 Triangle read by rows: T(n,k) = prime(n) mod A001223(k), where A001223 are differences between consecutive primes. %C A174433 The first prime gap is 3-2=1, so the first column is T(n,1)=0. The second and third prime gaps are 5-3=2 and 7-5=2, and since all primes > 2 are odd, T(n,2) = T(n,3) = 1. %e A174433 Triangle begins: %e A174433 0; %e A174433 0,1; %e A174433 0,1,1; %e A174433 0,1,1,3; %e A174433 0,1,1,3,1; %p A174433 A001223 := proc(n) ithprime(n+1)-ithprime(n) ; end proc: %p A174433 A174433 := proc(n,k) ithprime(n) mod A001223(k) ; end proc: %p A174433 seq(seq(A174433(n,k),k=1..n),n=1..14) ; %Y A174433 Cf. A000040. %K A174433 nonn,tabl %O A174433 1,10 %A A174433 _Juri-Stepan Gerasimov_, Nov 28 2010