Search results for "dist:Math-NumSeq Fibonacci"
Math::NumSeq::Fibonacci - Fibonacci numbers
The Fibonacci numbers F(i) = F(i-1) + F(i-2) starting from 0,1, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... starting i=0...
KRYDE/Math-NumSeq-75 - 04 Jun 2022 12:11:23 UTC
Math::NumSeq::FibonacciWord - 0/1 related to Fibonacci numbers
This is a sequence of 0s and 1s formed from the Fibonacci numbers. 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, ... starting i=0 The initial values are 0,1. Then Fibonacci number F(k) many values are copied from the start to extend, repeatedly. 0,...
KRYDE/Math-NumSeq-75 - 04 Jun 2022 12:11:23 UTC
Math::NumSeq::SpiroFibonacci - recurrence around a square spiral
This is the spiro-Fibonacci numbers by Neil Fernandez. The sequence is a recurrence SF[0] = 0 SF[1] = 1 SF[i] = SF[i-1] + SF[i-k] where the offset k is the closest point on the on the preceding loop of a square spiral. The initial values are 0, 1, 1,...
KRYDE/Math-NumSeq-75 - 04 Jun 2022 12:11:23 UTC
Math::NumSeq::FibonacciRepresentations - count of representations by sum of Fibonacci numbers
This is the Fibonacci representations function R(i) which is the number of ways i can be represented as a sum of distinct Fibonacci numbers, 1, 1, 1, 2, 1, 2, 2, 1, 3, 2, 2, 3, 1, 3, 3, 2, 4, 2, 3, 3, ... starting i=0 (OEIS A000119) For example R(11)...
KRYDE/Math-NumSeq-75 - 04 Jun 2022 12:11:23 UTC
Math::NumSeq::PisanoPeriod - cycle length of Fibonacci numbers mod i
This is the length cycle of Fibonacci numbers modulo i. 1, 3, 8, 6, 20, 24, 16, 12, 24, 60, 10, 24, 28, 48, 40, ... starting i=1 For example Fibonacci numbers modulo 4 repeat in a cycle of 6 numbers, so value=6. Fibonacci 0, 1, 1, 2, 3, 5, 8,13,21,34...
KRYDE/Math-NumSeq-75 - 04 Jun 2022 12:11:23 UTC
Math::NumSeq - number sequences
This is a base class for some number sequences. Sequence objects can iterate through values and some sequences have random access and/or a predicate test. The idea is to generate things like squares or primes in a generic way. Some sequences, like sq...
KRYDE/Math-NumSeq-75 - 04 Jun 2022 12:11:23 UTC
Math::NumSeq::PisanoPeriodSteps - Fibonacci frequency and Leonardo logarithm
This is the number of times the "PisanoPeriod" must be applied before reaching an unchanging value. 0, 4, 3, 2, 3, 1, 2, 2, 1, 2, 3, 1, 3, 2, 3, 1, 2, 1, 2, ... starting i=1 As per Fulton and Morris "On arithmetical functions related to the Fibonacci...
KRYDE/Math-NumSeq-75 - 04 Jun 2022 12:11:23 UTC
Math::NumSeq::Runs - runs of consecutive integers
This is various kinds of runs of integers. The "runs_type" parameter (a string) can be "0toN" 0, 0,1, 0,1,2, 0,1,2,3, etc runs 0..N "1toN" 1, 1,2, 1,2,3, 1,2,3,4, etc runs 1..N "1to2N" 1,2, 1,2,3,4, 1,2,3,4,5,6 etc runs 1..2N "1to2N+1" 1, 1,2,3, 1,2,...
KRYDE/Math-NumSeq-75 - 04 Jun 2022 12:11:23 UTC
Math::NumSeq::Pell - Pell numbers
The Pell numbers 0, 1, 2, 5, 12, 29, 70, 169, 408, 985, 2378, 5741, 13860, ... starting i=0 where P[k] = 2*P[k-1] + P[k-2] starting P[0]=0 and P[1]=1...
KRYDE/Math-NumSeq-75 - 04 Jun 2022 12:11:23 UTC
Math::NumSeq::Perrin - Perrin sequence
The Perrin sequence, 3, 0, 2, 3, 2, 5, 5, 7, 10, 12, 17, 22, 29, 39, 51, ... (A001608) which is the recurrence P(i) = P(i-2) + P(i-3) starting from 3,0,2. So for example 29 is 12+17. 12, 17, 22, 29 | | ^ | | | +---+---add-+...
KRYDE/Math-NumSeq-75 - 04 Jun 2022 12:11:23 UTC
Math::NumSeq::Fibbinary - without consecutive 1-bits
This sequence is the Fibbinary numbers 0, 1, 2, 4, 5, 8, 9, 10, 16, 17, 18, 20, 21, 32, 33, 34, ... starting i=0 (A003714) They have no adjacent 1-bits when written in binary, i Fibbinary Fibbinary (decimal) (binary) --- --------- -------- 0 0 0 1 1 ...
KRYDE/Math-NumSeq-75 - 04 Jun 2022 12:11:23 UTC
Math::NumSeq::Tribonacci - Tribonacci numbers
The Tribonacci sequence 0, 0, 1, 1, 2, 4, 7, 13, etc, T(i) = T(i-1) + T(i-2) + T(i-3) starting from 0,0,1....
KRYDE/Math-NumSeq-75 - 04 Jun 2022 12:11:23 UTC
Math::NumSeq::LucasNumbers - Lucas numbers
The Lucas numbers, L(i) = L(i-1) + L(i-2) starting from values 1,3. 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364,... starting i=1 This is the same recurrence as the Fibonacci numbers (Math::NumSeq::Fibonacci), but a different startin...
KRYDE/Math-NumSeq-75 - 04 Jun 2022 12:11:23 UTC
Math::NumSeq::FibbinaryBitCount - number of bits in each fibbinary number
The number of 1 bits in the i'th fibbinary number. 0, 1, 1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 3, 1, 2, 2, 2, 3, 2, ... starting i=0 For example i=9 is Fibbinary "1001" so value=2 for 2 1-bits. The count is 1 for the Fibonacci numbers, as they're "100..00" w...
KRYDE/Math-NumSeq-75 - 04 Jun 2022 12:11:23 UTC