Schuh, Fred. The master book of mathematical recreations. Translated by F. Göbel. Edited by T. H. Beirne. (English) Zbl 0191.27406 New York: Dover Publications, Inc. xvi, 430 p. (1968). Reviewer: H. Schubart Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 7 Documents MSC: 00A08 Recreational mathematics Keywords:general mathematics PDFBibTeX XML Online Encyclopedia of Integer Sequences: Josephus problem: numbers m such that, when m people are arranged on a circle and numbered 1 through m, the final survivor when we remove every 4th person is one of the first three people. Numbers k such that k and 2*k are anagrams. Numbers k such that k and 3*k are anagrams. Numbers k such that k and 5*k are anagrams. a(n) = ceiling((Sum_{k=1..n-1} a(k)) / 2) for n >= 2 starting with a(1) = 1. Subsequence of A005428 with state = 1. Subsequence of A005428 where state = 2. Numbers that have decimal expansion c(1)c(2)...c(n) with distinct digits that satisfy c(1) <> 0, c(1) is the largest digit, and for each i in 1..n there is j in 0..2 such that c(i) == 3*c(i-1) + j (mod 10) (with c(0): = c(n)). Numbers that have decimal expansion c(1)c(2)...c(n) with distinct digits that satisfy c(1) <> 0, c(1) is the largest digit, and for each i in 1..n there is j in {0, 1} such that c(i) == 2*c(i-1) + j (mod 10) (with c(0): = c(n)).