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 A057522 #19 Feb 16 2025 08:32:43 %S A057522 73,950,475,95,19,248,124,62,31,404,202,101,1314,657,219,73,950,475, %T A057522 95,19,248,124,62,31,404,202,101,1314,657,219,73,950,475,95,19,248, %U A057522 124,62,31,404,202,101,1314,657,219,73,950,475,95,19,248,124,62,31,404,202 %N A057522 a(n+1) = a(n)/2 if 2|a(n), a(n)/3 if 3|a(n), a(n)/5 if 5|a(n), a(n)/7 if 7|a(n), a(n)/11 if 11|a(n), otherwise 13*a(n)+1. %C A057522 This is the '13x+1' map. The 'Px+1 map': if x is divisible by any prime < P then divide out these primes one at a time starting with the smallest; otherwise multiply x by P and add 1. %H A057522 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CollatzProblem.html">Collatz problem</a> %H A057522 <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,1). %F A057522 For n>15, a(n) = a(n-15). [_Harvey P. Dale_, May 02 2011] %e A057522 73 -> 19*73+1 = 950, 950 = 2*5^2*19 -> 950/2 = 475, etc. %t A057522 nxt[n_]:=Which[Divisible[n,2],n/2,Divisible[n,3],n/3, Divisible[n,5], n/5, Divisible[n,7], n/7,Divisible[n,11],n/11,True,13n+1]; NestList[nxt,73,60] (* _Harvey P. Dale_, May 02 2011 *) %Y A057522 Cf. A057446 (short version), A057216, A057534, A057614. %K A057522 nonn %O A057522 0,1 %A A057522 Murad A. AlDamen (Divisibility(AT)yahoo.com), Oct 17 2000