Corpus ID: 216642194

Three Cousins of Recamán's Sequence

@article{Alekseyev2020ThreeCO,
  title={Three Cousins of Recam{\'a}n's Sequence},
  author={Max A. Alekseyev and Joseph Samuel Myers and Richard Schroeppel and Scott R. Shannon and N. J. A. Sloane and Paul Zimmermann},
  journal={arXiv: Number Theory},
  year={2020}
}
Although 10^230 terms of Recaman's sequence have been computed, it remains a mystery. Here three distant cousins of that sequence are described, one of which is also mysterious. (i) {A(n), n >= 3} is defined as follows. Start with n, and add n+1, n+2, n+3, ..., stopping after adding n+k if the sum n + (n+1) + ... + (n+k) is divisible by n+k+1. Then A(n)=k. We determine A(n) and show that A(n) = 1} is a multiplicative analog of {A(n)}. Start with n, and successively multiply by n+1, n+2… Expand

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SHOWING 1-10 OF 22 REFERENCES
ON THE REPRESENTATION OF THE INTEGERS AS A DIFFERENCE OF NONCONSECUTIVE TRIANGULAR NUMBERS
The problem of determining the set of integer solutions of a polynomial equation, over Z, occurs frequently throughout much of the theory of numbers. Typically, the most common form of these problemsExpand
Speeding up Integer Multiplication and Factorization
This thesis explores improvements to well-known algorithms for integer multiplication and factorization. The Schonhage-Strassen algorithm for integer multiplication, published in 1971, was the firstExpand
Smooth numbers: computational number theory and beyond
The analysis of many number theoretic algorithms turns on the role played by integers which have only small prime factors; such integers are known as “smooth numbers”. To be able to determine whichExpand
A note on Sierpiński's problem related to triangular numbers
In this note we show that the system of equations tx + ty = tp, ty + tz = tq, tx + tz = tr, where tx = x(x + 1)/2 is a triangular number, has infinitely many solutions in integers. Moreover we showExpand
A course in computational algebraic number theory
  • H. Cohen
  • Computer Science, Mathematics
  • Graduate texts in mathematics
  • 1993
TLDR
The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods. Expand
Pythagorean triples and sums of triangular numbers
Each primitive Pythagorean triple of positive integers leads, with the aid of an algebraic identity, to a family of triples of integers. Each triple in this family provides three triangular numbers,Expand
Explaining the wheel sieve
  • P. Pritchard
  • Mathematics, Computer Science
  • Acta Informatica
  • 2004
TLDR
A simple mathematical framework is developed, which leads to a smoother and more insightful derivation of the new algorithm, and which may be of independent interest to the number theorist. Expand
A hyperelliptic smoothness test. I
This series of papers is concerned with a probabilistic algorithm for finding small prime factors of an integer. While the algorithm is not practical, it yields an improvement over previousExpand
An introduction to the theory of numbers
Divisibility congruence quadratic reciprocity and quadratic forms some functions of number theory some diophantine equations Farey fractions and irrational numbers simple continued fractions primesExpand
A Note on triangular numbers
  • Punjab University J. Math., 26
  • 1993
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2
3
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