PrimeProductsMinusOne

Positions i with i * p(i) - 1 prime.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt001287via Permutation✓↗

PrimeProductsMinusOne(p)Positions i with i * p(i) - 1 prime.

Typed signatures

Type	Package	Applies
(permutation) -> number	combinatorics	always

Domain: Permutation statistics

Details

• Defined over Permutation as an expression in _x, evaluated by compute-engine — the definition IS the implementation.
• Takes a Permutation and nothing else — it reads values against their positions, or walks the orbits, so it needs the bijection. Applying it to a bare list is a type error, not a wrong answer.

Definition

Epsil, as the implementation runs it.

on Permutation, over _x

0 if Length(_x) < 1 else Count(Filter(
                                       Range(1, Length(_x)),
                                       Function(i * _x[i] - 1 >= 2 && Count(Filter(
                                                                                    Range(2, i * _x[i] -
                                                                                             1),
                                                                                    Function(d <
                                                                                             i * _x[i] -
                                                                                             1 &&
                                                                                             (i * _x[i] -
                                                                                              1) %
                                                                                             d ==
                                                                                             0, d),
                                                                                  )) ==
                                                                      0, i),
                                     ))

Examples

Basic #

the one-line word $312$

live ↗

In$\mathrm{PrimeProductsMinusOne}({\operatorname{Permutation}}([3, 1, 2]))$Out$2$

the one-line word $2413$

live ↗

In$\mathrm{PrimeProductsMinusOne}({\operatorname{Permutation}}([2, 4, 1, 3]))$Out$3$

Properties #

FindStat's value for [1]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{Permutation}}([1]), \text{PrimeProductsMinusOne})$Out$0$

Known value · FindStat St001287

FindStat's value for [1,2]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{Permutation}}([1, 2]), \text{PrimeProductsMinusOne})$Out$1$

Known value · FindStat St001287

FindStat's value for [2,1]

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{Permutation}}([2, 1]), \text{PrimeProductsMinusOne})$Out$0$

Known value · FindStat St001287

About

Examples	5
Crosswalk	FindStat