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 A203907 #29 Feb 16 2025 08:33:16
%S A203907 55,15,165,30,275,45,1,60,495,75,13,90,11,105,825,120,1,135,77,150,3,
%T A203907 26,95,180,1375,22,1485,210,77,225,1705,240,29,2,5,270,2035,23,33,300,
%U A203907 2255,315,2365,52,2475,190,2585,360,7,375,19,44,2915,405,65,420
%N A203907 Successor function for Conway's PRIMEGAME.
%C A203907 a(n) <= 55 * n, as 55/1 is the last and largest FRACTRAN fraction.
%C A203907 Iterations, starting with 2, give A007542. A185242 begins with 3.
%C A203907 A quasipolynomial of order 6469693230 = 29#. - _Charles R Greathouse IV_, Jul 31 2016
%C A203907 Apparent simple regularities do not necessarily hold. It is true that a(2n)/15 = a(4n)/30, but for n = 11, 13, 17, 19, 22, 23, ... this is not equal to n. Also, a(2k-1) = 55k holds for more than 60%, but not for all k >= 1. - _M. F. Hasler_, Jun 15 2017
%H A203907 Reinhard Zumkeller, <a href="/A203907/b203907.txt">Table of n, a(n) for n = 1..10000</a>
%H A203907 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FRACTRAN.html">FRACTRAN</a>
%H A203907 Wikipedia, <a href="https://oeis.org/wiki/Conway's_PRIMEGAME">Conway's PRIMEGAME</a>
%F A203907 Let [17/91, 78/85, 19/51, 23/38, 29/33, 77/29, 95/23, 77/19, 1/17, 11/13, 13/11, 15/2, 1/7, 55/1] be the list of FRACTRAN fractions = [A202138(k)/A203363(k) : 1<=k<=14], then a(n) = n*f, where f is the first term yielding an integral product.
%t A203907 conwayFracs = {17/91, 78/85, 19/51, 23/38, 29/33, 77/29, 95/23, 77/19, 1/17, 11/13, 13/11, 15/2, 1/7, 55}; conwayProc[n_] := Module[{curr = 1/2, iter = 1}, While[Not[IntegerQ[curr]], curr = conwayFracs[[iter]]n; iter++]; Return[curr]]; Table[conwayProc[n], {n, 60}] (* _Alonso del Arte_, Jan 24 2012 *)
%o A203907 (Haskell)
%o A203907 import Data.Ratio ((%), numerator, denominator)
%o A203907 a203907 n = numerator $ head
%o A203907 [x | x <- map (* fromInteger n) fracts, denominator x == 1]
%o A203907 where fracts = zipWith (%) a202138_list a203363_list
%o A203907 a203907_list = map a203907 [1..]
%o A203907 (PARI) {A203907(n,V=[17/91, 78/85, 19/51, 23/38, 29/33, 77/29, 95/23, 77/19, 1/17, 11/13, 13/11, 15/2, 1/7, 55])=for(i=1,#V, denominator(V[i]*n)==1 && return(V[i]*n))} \\ _Charles R Greathouse IV_, Jul 31 2016, edited by _M. F. Hasler_, Jun 15 2017
%Y A203907 Cf. A007542.
%K A203907 nonn,easy,nice
%O A203907 1,1
%A A203907 _Reinhard Zumkeller_, Jan 24 2012