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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
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
KEYWORD
nonn
AUTHOR
John W. Layman, Mar 20 2003
STATUS
approved