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 A080209 #18 Feb 16 2025 08:32:48
%S A080209 2,1,1,3,1,1,1,3,1,1,1,1,3,1,1,3,1,3,1,1,1,1,3,1,3,1,3,1,3,1,3,1,3,1,
%T A080209 1,1,3,1,3,1,1,3,1,1,1,1,1,3,1,1,3,1,3,1,1,3,1,3,1,3,1,3,1,1,3,1,1,1,
%U A080209 1,1,3,1,1,1,1,1,1,3,1,3,1,1,1,3,1,3,1,1,1,1,3,1,3,1,3,1,3,1,3,1,1,3,1,1,3
%N A080209 Gilbreath transform of the sequence of Sophie Germain primes (A005384), i.e., the diagonal of leading successive absolute differences of A005384.
%C A080209 Conjecture: The diagonal of leading successive absolute differences of the Sophie Germain primes consists, except for the initial 2, only of 1's and 3s.
%H A080209 Cristian Cobeli, Mihai Prunescu, Alexandru Zaharescu, <a href="http://arxiv.org/abs/1511.04315">A growth model based on the arithmetic Z-game</a>, arXiv:1511.04315 [math.NT], 2015.
%H A080209 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SophieGermainPrime.html">Sophie Germain Prime.</a>
%H A080209 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GilbreathsConjecture.html">Gilbreath's Conjecture</a>
%e A080209 The difference table begins:
%e A080209 2;
%e A080209 3, 1;
%e A080209 5, 2, 1;
%e A080209 11, 6, 4, 3;
%e A080209 23, 12, 6, 2, 1;
%e A080209 29, 6, 6, 0, 2, 1;
%t A080209 sgp[1] = Select[Prime[Range[1000]], PrimeQ[2 # + 1]&];
%t A080209 sgp[n_] := Differences[sgp[n - 1]] // Abs;
%t A080209 Table[sgp[n], {n, 1, 105}][[All, 1]] (* _Jean-François Alcover_, Feb 04 2019 *)
%Y A080209 Cf. A005384, A036262, A054977.
%K A080209 nonn
%O A080209 1,1
%A A080209 _John W. Layman_, Mar 20 2003