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.

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

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