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A080209
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Gilbreath transform of the sequence of Sophie Germain primes (A005384), i.e., the diagonal of leading successive absolute differences of A005384.
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0
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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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
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EXAMPLE
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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;
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A005384, A036262, A054977.
Sequence in context: A283495 A196931 A175465 * A347171 A127949 A167407
Adjacent sequences: A080206 A080207 A080208 * A080210 A080211 A080212
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KEYWORD
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nonn
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AUTHOR
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John W. Layman, Mar 20 2003
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STATUS
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approved
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