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CALKIN-WILF SEQUENCES FOR IRRATIONAL NUMBERS

期刊: FIBONACCI QUARTERLY, 2023; 61 (1)

We generalize the Calkin-Wilf sequence by applying its recursion formula to an irrational initial value. We prove that if we start with quadratic surd......

ON INTEGERS WHOSE SUM IS THE REVERSE OF THEIR PRODUCT

期刊: FIBONACCI QUARTERLY, 2023; 61 (1)

We determine all pairs of positive integers (a, b) such that a + b and a x b have the same decimal digits in reverse order: (2, 2), (9, 9), (3, 24), (......

SUMS OF FIBONACCI NUMBERS INDEXED BY INTEGER PARTS

期刊: FIBONACCI QUARTERLY, 2023; 61 (2)

Consider the integer sequences (F-root n:n is an element of N0) and (Flog2n:n is an element of N), lettingx denote the integer part of a nonnegative v......

ADVANCED PROBLEMS AND SOLUTIONS

期刊: FIBONACCI QUARTERLY, 2023; 61 (3)

Please send all communications concerning ADVANCED PROBLEMS AND SOLUTIONS to Robert Frontczak, LBBW, Am Hauptbahnhof 2, 70173 Stuttgart, Germany, or b......

FIBONACCI OR LUCAS NUMBERS THAT ARE CONCATENATIONS OF TWO g-REPDIGITS

期刊: FIBONACCI QUARTERLY, 2023; 61 (1)

Let k >= 1 and g >= 2 be positive integers. Any positive integer N of the form ------------------------------------------- N = d(1)... d(1) d(2)......

ADDITIONAL SUMS INVOLVING GIBONACCI POLYNOMIALS

期刊: FIBONACCI QUARTERLY, 2023; 61 (1)

We continue the exploration of sums involving gibonacci polynomials and their numeric versions, and their Pell versions.

SUMS INVOLVING TWO CLASSES OF GIBONACCI POLYNOMIALS

期刊: FIBONACCI QUARTERLY, 2023; 61 (4)

We explore six infinite sums involving gibonacci polynomial squares and their implications.

INFINITE SUMS INVOLVING JACOBSTHAL POLYNOMIALS: GENERALIZATIONS

期刊: FIBONACCI QUARTERLY, 2023; 61 (4)

We explore the Jacobsthal versions of four infinite sums involving gibonacci polynomials.

SUMS INVOLVING GIBONACCI POLYNOMIAL SQUARES REVISITED

期刊: FIBONACCI QUARTERLY, 2023; 61 (2)

We explore four infinite sums involving a special class of gibonacci polynomial squares.

A NOTE ON THE FIBONACCI SEQUENCE AND SCHREIER-TYPE SETS

期刊: FIBONACCI QUARTERLY, 2023; 61 (3)

A set A of positive integers is said to be Schreier if either A=& empty;or min A >=|A|. We give a bijective map to prove the recurrence of the ......

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