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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

Table of n, a(n) for n=1..105.

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-Fran├žois 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.)