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 A080209 Gilbreath transform of the sequence of Sophie Germain primes (A005384), i.e., the diagonal of leading successive absolute differences of A005384. 0
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. LINKS Cristian Cobeli, Mihai Prunescu, Alexandru Zaharescu, A growth model based on the arithmetic Z-game, arXiv:1511.04315 [math.NT], 2015. Eric Weisstein's World of Mathematics, Sophie Germain Prime. Eric Weisstein's World of Mathematics, Gilbreath's Conjecture EXAMPLE The difference table begins:    2;    3,  1;    5,  2,  1;   11,  6,  4,  3;   23, 12,  6,  2,  1;   29,  6,  6,  0,  2,  1; MATHEMATICA sgp[1] = Select[Prime[Range[1000]], PrimeQ[2 # + 1]&]; sgp[n_] := Differences[sgp[n - 1]] // Abs; Table[sgp[n], {n, 1, 105}][[All, 1]] (* Jean-François Alcover, Feb 04 2019 *) CROSSREFS Cf. A005384, A036262, A054977. Sequence in context: A283495 A196931 A175465 * A347171 A127949 A167407 Adjacent sequences:  A080206 A080207 A080208 * A080210 A080211 A080212 KEYWORD nonn AUTHOR John W. Layman, Mar 20 2003 STATUS approved

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Last modified May 28 18:24 EDT 2022. Contains 354122 sequences. (Running on oeis4.)