FunWithNumbers (version 1.2)

vaneck: Generate a sequence 'invented' by Jan Ritsema Van Eck

Description

This function generates an interesting (to the author, at least) sequence listed as number A181391 in the https://oeis.org/. See Details for a full description.

Usage

vaneck(howlong = 100, ve = NULL, ...)

Value

ve

The vector (ve for "VanEck") of the sequence values calculated

uniqs

a vector of the unique values in ve

Arguments

howlong

How many terms to generate.

ve

Optional argument. Enter a previously generated ("VanEck") sequence here as a numeric vector, or a single integer to use as an initiator.

...

reserved for possible future use.

Author

Carl Witthoft,

Details

The rule here is that you start with 0, and whenever you get to a number you have not seen before, the following term is a 0. But if the number k has appeared previously in the sequence, then you count the number of terms since the last appearance of k, and that number is the following term. In more detail:

Term 1: The first term is 0 by definition. Term 2: Since we havent seen 0 before, the second term is 0. Term 3: Since we have seen a 0 before, one step back, the third term is 1 Term 4: Since we havent seen a 1 before, the fourth term is 0 Term 5: Since we have seen a 0 before, two steps back, the fifth term is 2. And so on. As of this release of this R-package, how fast max(sequence) grows, and whether every number eventually appears, are open questions. The latest investigations and theorems related to this sequence can be found at https://oeis.org/A181391/

References

https://oeis.org/A181391/

Examples

(vaneck(20))
# $ve
#  [1] 0 0 1 0 2 0 2 2 1 6 0 5 0 2 6 5 4 0 5 3 0
# $uniqs
# [1] 0 1 2 6 5 4 3