This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A058047 #38 Feb 16 2025 08:32:43 %S A058047 3,5,7,29,41,79 %N A058047 Generalized Collatz sequences: primes resulting in a cycle containing 1. %C A058047 For each prime P check the generalized Collatz sequence of each integer N > 1 defined by c(1) = N, c(n+1) = c(n) * P + 1 if F > P, otherwise c(n+1) = c(n) / F, where F is the smallest factor of c(n), until c(n) = c(m) for n > m starts a cycle. If all c(i) > 1, then P does not belong to the sequence (and vice versa). %C A058047 All terms are as yet only conjectures. _Jeff Heleen_ checked the primes < 1000 and start points up to 10000000 (see Prime Puzzle 114 and example below). a(1)=3 is the ordinary Collatz problem. - _Frank Ellermann_, Jan 20 2002 %C A058047 The jOEIS program uses start points up to 10^8 and yields [3, 5, 7, 19, 29, 41, 43*, 53, 71*, 79, 89*, 103*, 107, 109*, 127, 131*, 137] followed by [139, 149, 157, 179, 191, 197, 199, 211, 227, ...]. The terms in the first list without asterisks agree with A106919. - _Georg Fischer_, Jun 17 2023 %H A058047 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a058/A058047.java">Java program</a> in the jOEIS project. %H A058047 Randall L. Rathbun, <a href="/A058047/a058047.txt">Discussion of this sequence</a> %H A058047 Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_114.htm">Puzzle 114. The Murad's generalization of the Collatz's sequences</a>, The Prime Puzzles & Problems Connection. %H A058047 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CollatzProblem.html">Collatz problem</a> %e A058047 a(4) > 11, e.g.: 17, 17*11 + 1 = 188, 188/(2*2) = 47, 47*11 + 1 = 518, 518/(2*7) = 37, 37*11 + 1 = 408, 408/(2*2*2*3) = 17 (cycle without 1). %e A058047 For p = 29 e.g.: 17, 17*29 + 1 = 494, 494/(2*13*19) = 1, 1*29 + 1 = 30, 30/30 = 1 (cycle with 1), no counterexample below 10000000. %o A058047 (Java) Cf. link to the program in the jOEIS project. %Y A058047 Cf. A057216, A057446, A057534, A057614, A058048, A106919. %K A058047 nonn,more %O A058047 0,1 %A A058047 Murad A. AlDamen (Divisibility(AT)yahoo.com), Nov 17 2000 %E A058047 Edited by _Frank Ellermann_, Jan 20 2002