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Problem hidden on 2015-04-04 18:20:38 by Francky

FRANCKY - Francky homepage

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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 σ0(n) is the product of two primes only.
Divisors : Print numbers such σ0(n)>3 and (m|n ⇒ σ0(m)|σ0(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.


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).


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)

Added by:Francky
Time limit:20s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)