**hidden**on 2015-04-04 18:20:38 by

*Francky*

## FRANCKY - Francky homepage

**Content:**

## My favorite problems

### Prime numbers

Super Primes : A very good tutorial problem, not easy with Python.

Prime Intervals : An excellent tutorial problem, not easy with Python.

Printing some primes

Printing some primes (Hard)

Finding the Kth Prime.

Prime after N : Do you have a good next_prime function? Doable in Python.

Prime Again : Do you have a good previous_prime function? Hard with Python.

Fun With Primes : Not so easy in Python.

Obsession : Primes of the form 2k²-1.

Bazinga! : Product of only two primes.

Prime Number Theorem : Calculate the percent error |π(x) - x/lnx| / π(x) %.

Divisors : Print numbers such σ_{0}(n) is the product of two primes only.

Divisors : Print numbers such σ_{0}(n)>3 and
(m|n ⇒ σ_{0}(m)|σ_{0}(n)).

Prime checker : THE prime testing challenge!

### Factorization (or almost)

Medium Factorization : 7 digits.

Integer Factorization : 15 digits.

Integer Factorization : 20 digits.

Integer Factorization : 29 digits.

Number of common divisors.

Euler Totient Function.

Divisor Summation (Hard).

Number Theory : unsolved.

Square Free Factorization : Smallest number of square-free factors.

Almost square factorisation.

Homework : Reduce sqrt(N) in A×SQRT(B), with maximum A.

Fibonacci Factor.

### Recursive sequence

Recursive SequenceNot easy using Python.

Recursive Sequence (Version II) : My favorite problem on that kind.

Nacci Fear : The next best one.

Pibonacci : P(x)=1 if x<4 else P(x-1)+P(x-π) .

Hofstadter–Conway 10000 dollar sequence : a summatory function.

Recurrence : Arithmetico-geometric sequence.

(Also see Aritho-geometric Series (AGS).)

(Also see Speed test - Cube version.)

Grid Tiling with 4 kind of colored pieces.

Blocks for kids with 4 kind of pieces.

Snaky Numbers.

R Numbers.

Fun with numbers.

Easy Sequence! : F(n) = [F(n-1)*F(n-2)]^K.

Sum of products.

Just Add It.

### Fibonacci

Flibonakki : my favorite FIB-like problem.

Sum of Tetranacci numbers : My second one.

Fibonacci Sum of consecutive terms.

Fibonacci With a Square Root.

Arya Rage : modular 2^fib(n-1).

### Polynomials

Fibonacci vs Polynomial (HARD).

A Summatory (HARD).

Polynomial f(x) to Polynomial h(x).

Power Sums.

### Ad hoc

det( gcd(i,j)^k, (i,j) ) .

Legendre symbol.

GHALIBS CHALLENGE : Count marbles arrangements... (hard)

Upper Right King (Hard) : King's move on chessboard.

Toward Infinity : Sum from n = 1 to infinity of n^k / r^n.

A Famous Stone Collector.

New Game with a Chess Piece : Other moves on chessboard.

Travelling Knight : Knight moves on chessboard.

Card Game.

Starship : floats.

Factorial : Number of zeros at the end of N! .

Last Non-Zero Digit of Factorials.

Product of factorials (medium).

K12-Combinations : A squared binomial sum.

Power with Combinatorics.

Power with Combinatorics(HARD).

Matrix inversion.

UFO : Shortest path, circle, float.

Three Circle Problem
(easy),
(hard) : Circles, tangents.

Colorful Circle (EASY) : count ways to color sectors.

Card Shuffling : order of a permutation.

Yet Another Permutations Problem : Counts some permutations.

Polygon diagonals : Polygon Diagonals,
Divide Polygon,
Divide Polygon (HARD) : number of ways to draw diagonals.

Conga line : Shortest time to rearrange dancers.

Blueberries : Maximum number of blueberries you can grab.

The One-Dimensional Pool Table : In-line elastic collisions.

Ninja : Dividing a cube.

Enough of analyzing, let's play : Play game of Nim.

Team Nim : 4 players for game of Nim.

SelfDescribingSequenceProblem : Golomb.

Discord is at it again : a sequence without any 5.

Movie Theater Madness : a story of height.

Power Tower City : Knuth's up-arrow notation.

Brute-force Algorithm EXTREME : Counting function calls.

Spy : a Blue.Mary very nice problem.

...

## My own problems

(2012-05-26) The return of the Cake : Is trisection possible?

(2012-05-26) With a Pit of Death : Tiling (N×M) problem with a hole. Is it possible or not?

(2012-06-14) The dojo's corridor : With a tiling problem ; shorten challenge.

(2012-07-06) DOJO Corridor I : Tiling problem ([1..4] × N, with a hole).

(2012-07-08) DOJO Corridor II : Tiling problem (5 × N, with a hole).

(2012-08-19) Fibonaccibonacci (easy) : Modular computation of FIB( FIB(N) ).

(2012-08-19) Fibonacci recursive sequences (medium) : Modular computation of FIB(... FIB( FIB(N) ) ...).

(2012-08-19) Fibonacci recursive sequences (hard) : Modular computation of FIB(... FIB( FIB(N) ) ...).

(2012-11-11) Pell (Mid pelling) : Solve the Pell equation.

(2012-11-23) Print Big Binary Numbers : Warning you need fast bignum multiplication method.

(2012-12-01) Pell Fourth : Find and solve worst cases for Pell equation. Challenge.

Solve phi(n) in perm(n) with minimal n/phi(n),

(2013-01-06) Totient in permutation (easy) : with n<10^7.

(2013-01-06) Totient in permutation (medium) : with <10^12.

(2013-01-06) Totient in permutation (hard) : with n<10^27.

(2013-01-20) Fibonacci factorization : The Mysterious Affair at Byte Court.

(2013-01-20) Modular Fibonacci Period : For M<10^12.

(2013-01-20) Fimodacci : Compute Fib(N) mod Fib(K).

(2013-01-20) 64bit-Fibonacci : Compute Fib(N) mod M, with M < 10^18. Speed challenge.

(2013-01-26) Card Meets (medium) : Derangement unless one.

(2013-02-03) Factor y Hell : Number of zeros at the end of Factorial(N) written in a given base.

(2013-02-19) Tjandra 19th birthday present (HARD) : Combinatorial, ad hoc.

(2013-02-22) The SPP constant challenge : Speed challenge, recursive sequence of low order.

(2013-02-27) Matrix Exponentiation : Speed challenge, modular power of a matrix (order 18).

Number of ways to form homogeneous teams.

(2013-03-03) Thousands ByteMan March : Medium constraints.

(2013-03-03) Billion ByteMan March : Hard constraints.

(2013-03-16) Amazing Factor Sequence (medium) : Sum of sum of divisors.

(2013-03-17) Power Factor Sum Sum (hard) : Sum of sum of powered divisors.

(2013-03-17) Pythagorean triplets : Number of Pythagorean triplet {a,b,c} such that N ≤ a,b,c ≤ M.

(2013-04-19) Shared cathetus (easy) : Number of ways in which n can be the cathetus (leg) of a Pythagorean triangle.

(2013-04-19) Delta catheti (hard) : Find the nth Pythagorean triplet {a,b,c} such that b-a=d; answer modulo m.

(2013-04-21) Delta catheti II (Hard) : Same as previous but harder constraints. My hardest problem for sure!

(2013-04-30) Almost-isosceles Pythagorean triple (easy) : The easy case when delta = 1.

...

(2014-03-01) Product of factorial (easy)

(2014-03-01) Product of factorial (again)

(2014-03-01) Product of factorial (hard)

(2014-03-03) Boring Factorials (Reloaded)

(2014-03-04) Boring Factorials (Extended)

(2014-03-04) Boring Factorials (Challenge)

...

(2014-03-09) Sum of Prime : a speed challenge.

(2014-03-09) Sum of Prime (reverse mode)

(2014-03-17) Huge Pascal triangle

(2014-03-19) Base Conversion

...

(2014-03-23) Modular Bernoulli: numerator of Bernoulli numbers modulo a small prime.

(2014-03-23) Power Sum: as a challenge

(2014-04-05) Fibonacci Power Sum: another challenge

(2014-04-05) Fibonacci extraction Sum

(2014-05-04) Modular Tetration

(2014-05-14) Psycho34 (easy) : partial factorization of small numbers

(2014-06-01) Travelling Knight 2

(2014-06-04) Counting triangles 2

About some linear recursive sequences:

(2014-06-04) 100pct failure within 72 hours

(2014-06-07) Moon Safari (easy)

(2014-06-07) Moon Safari (medium)

(2014-06-07) Moon Safari (Hard)

[2014-06-09 Accident, surgery,... ]

(2014-12-12) Prime Power Test

(2014-12-13) Prime Power Test (Hard)

(2014-12-29) Euler Totient Function Sieve

(2014-12-29) Periodic function, trip1

(2014-12-29) Periodic function, trip2

(2015-01-05) Periodic function, trip3

(2015-01-05) Periodic function, trip3 (easy)

(2015-01-17) Divisors of factorial (medium)

(2015-01-18) Divisors of factorial (hard)

(2015-01-24) Smallest Number (medium)

[2015-04-10 surgery (part 2) ,... ]

(2016-06-09) Periodic function, trip 5

(2016-06-28) 2D arrays with XOR property

(2016-07-16) Divisible Fibonacci Numbers

(2016-07-21) Zeros of the fundamental Fibonacci period

(2016-??-??) Previous Prime (64 bit edition)

(2016-??-??) Previous Prime (128 bit edition)

## Contact me

Math teacher in the south of France, middle and high school.

francky.spoj@gmx.com

Francky & Facebook

Also interested in MTB, para-gliding, windsurf, and mountain in general.

Added by: | Francky |

Date: | 2012-11-06 |

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Cluster: | Cube (Intel G860) |

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