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%I #17 Feb 05 2019 03:14:52
%S 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 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 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 Gilbreath transform of the sequence of Sophie Germain primes (A005384), i.e., the diagonal of leading successive absolute differences of A005384.
%C 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 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SophieGermainPrime.html">Sophie Germain Prime.</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GilbreathsConjecture.html">Gilbreath's Conjecture</a>
%e The difference table begins:
%e 2;
%e 3, 1;
%e 5, 2, 1;
%e 11, 6, 4, 3;
%e 23, 12, 6, 2, 1;
%e 29, 6, 6, 0, 2, 1;
%t sgp[1] = Select[Prime[Range[1000]], PrimeQ[2 # + 1]&];
%t sgp[n_] := Differences[sgp[n - 1]] // Abs;
%t Table[sgp[n], {n, 1, 105}][[All, 1]] (* _Jean-François Alcover_, Feb 04 2019 *)
%Y Cf. A005384, A036262, A054977.
%K nonn
%O 1,1
%A _John W. Layman_, Mar 20 2003
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