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The ``comma sequence'' starts with 1 and is defined by the property that if k and k' are consecutive terms, the two-digit number formed from the last digit of k and the first digit of k' is equal to the difference k'-k. If there is more than one such
Externí odkaz:
http://arxiv.org/abs/2401.14346
Autor:
Sloane, N. J. A., Theobald, Gavin A.
What is the smallest number of pieces that you can cut an n-sided regular polygon into so that the pieces can be rearranged to form a rectangle? Call it r(n). The rectangle may have any proportions you wish, as long as it is a rectangle. The rules ar
Externí odkaz:
http://arxiv.org/abs/2309.14866
Autor:
Sloane, N. J. A.
Until 1973 there was no database of integer sequences. Someone coming across the sequence 1, 2, 4, 9, 21, 51, 127,... would have had no way of discovering that it had been studied since 1870 (today these are called the Motzkin numbers, and form entry
Externí odkaz:
http://arxiv.org/abs/2301.03149
The Binary Two-Up Sequence is the lexicographically earliest sequence of distinct nonnegative integers with the property that the binary expansion of the n-th term has no 1-bits in common with any of the previous floor(n/2) terms. We show that the se
Externí odkaz:
http://arxiv.org/abs/2209.04108
Autor:
Alekseyev, Max A., Sloane, N. J. A.
Publikováno v:
Journal of Combinatorics and Number Theory 12:3 (2022), 115-155
A base-b junction number u has the property that there are at least two ways to write it as u = v + s(v), where s(v) is the sum of the digits in the expansion of the number v in base b. For the base-10 case, Kaprekar in the 1950's and 1960's studied
Externí odkaz:
http://arxiv.org/abs/2112.14365
Autor:
Sloane, N. J. A.
An introduction to the On-Line Encyclopedia of Integer Sequences (or OEIS, https://oeis.org) for graduate students in mathematics
Comment: 4 pages, 5 references
Comment: 4 pages, 5 references
Externí odkaz:
http://arxiv.org/abs/2105.05111
A survey of enumeration problems arising from the study of graphs formed when the edges of a polygon are marked with evenly spaced points and every pair of points is joined by a line. A few of these problems have been solved, a classical example bein
Externí odkaz:
http://arxiv.org/abs/2009.07918
Autor:
Alekseyev, Max A., Myers, Joseph Samuel, Schroeppel, Richard, Shannon, S. R., Sloane, N. J. A., Zimmermann, Paul
Publikováno v:
Fibonacci Quart. 60:3 (2022), 201-219
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
Externí odkaz:
http://arxiv.org/abs/2004.14000
Number the cells of a (possibly infinite) chessboard in some way with the numbers 0, 1, 2, ... Consider the cells in order, placing a queen in a cell if and only if it would not attack any earlier queen. The problem is to determine the positions of t
Externí odkaz:
http://arxiv.org/abs/1907.09120
The "Choix de Bruxelles" operation replaces a positive integer n by any of the numbers that can be obtained by halving or doubling a substring of the decimal representation of n. For example, 16 can become any of 16, 26, 13, 112, 8, or 32. We investi
Externí odkaz:
http://arxiv.org/abs/1902.01444