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A212990
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Number of iterations needed to reach 1 when computing repeatedly absolute values of differences of the sequence "2, followed by consecutive primes beginning with the n-th prime". a(n)=0 if 1 is never reached.
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2
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1, 2, 2, 9, 7, 14, 10, 17, 21, 27, 32, 43, 35, 32, 43, 48, 50, 54, 59, 78, 71, 69, 48, 75, 74, 100, 80, 85, 77, 115, 105, 110, 102, 137, 139, 147, 148, 159, 156, 186, 151, 144, 156, 166, 167, 148, 222, 233, 209, 247, 214, 219, 249, 245, 226, 241, 234, 267, 243, 233, 256, 292, 290, 269, 283
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OFFSET
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2,2
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COMMENTS
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We conjecture that a(n)>0, and that after reaching the first 1, all further iterations begin with 1. This is a generalization of the well known Gilbreath's conjecture. We call the effect, that a "tail" of 1's appears after a time, "lizard's effect for primes" (see seqfan list from Jun 01 2012).
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LINKS
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Alois P. Heinz and Zak Seidov, Table of n, a(n) for n = 2..1000 (first 500 terms from Alois P. Heinz)
Eric Weisstein's World of Mathematics, Gilbreaths Conjecture
Wikipedia, Gilbreaths Conjecture
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FORMULA
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Conjecture: limsup a(n)/prime(n) = 1.
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EXAMPLE
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Let n=6, prime(6) = 13. Then we consider the sequences of primes and iterations of absolute values of differences:
2, 13, 17, 19, 23, 29, 31, 37, ...
11, 4, 2, 4, 6, 2, 6, ...
7, 2, 2, 2, 4, 4, ...
5, 0, 0, 2, 0, ...
5, 0, 2, 2, ...
5, 2, 0, ...
3, 2, ...
1, ...
Thus the number of the first iteration beginning with 1 is 7, and a(6)=7.
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CROSSREFS
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Cf. A036262.
Sequence in context: A005168 A256591 A011149 * A220265 A243597 A021439
Adjacent sequences: A212987 A212988 A212989 * A212991 A212992 A212993
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KEYWORD
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nonn
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AUTHOR
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Vladimir Shevelev, Jun 01 2012
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EXTENSIONS
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More terms from Graeme McRae and Peter J. C. Moses
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STATUS
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approved
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