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A212990 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. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

COMMENTS

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).

LINKS

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

FORMULA

Conjecture: limsup a(n)/prime(n) = 1.

EXAMPLE

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.

CROSSREFS

Cf. A036262.

Sequence in context: A005168 A256591 A011149 * A220265 A243597 A021439

Adjacent sequences:  A212987 A212988 A212989 * A212991 A212992 A212993

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Jun 01 2012

EXTENSIONS

More terms from Graeme McRae and Peter J. C. Moses

STATUS

approved

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Last modified June 27 11:25 EDT 2017. Contains 288788 sequences.