A080209 Gilbreath transform of the sequence of Sophie Germain primes (A005384), i.e., the diagonal of leading successive absolute differences of A005384.

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

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-François Alcover, Feb 04 2019 *)

Crossrefs

Cf. A005384, A036262, A054977.

Sequence in context: A283495 A196931 A175465 * A347171 A127949 A051340

Adjacent sequences: A080206 A080207 A080208 * A080210 A080211 A080212

Keyword

nonn

Author

John W. Layman, Mar 20 2003

Status

approved