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.

73, 950, 475, 95, 19, 248, 124, 62, 31, 404, 202, 101, 1314, 657, 219, 73, 950, 475, 95, 19, 248, 124, 62, 31, 404, 202, 101, 1314, 657, 219, 73, 950, 475, 95, 19, 248, 124, 62, 31, 404, 202, 101, 1314, 657, 219, 73, 950, 475, 95, 19, 248, 124, 62, 31, 404, 202

Offset: 0

Author

Murad A. AlDamen (Divisibility(AT)yahoo.com), Oct 17 2000

Keywords

• nonn

Comments

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.

Examples

			73 -> 19*73+1 = 950, 950 = 2*5^2*19 -> 950/2 = 475, etc.
		

Links

• Eric Weisstein's World of Mathematics, Collatz problem
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).

Crossrefs

Cf. A057446 (short version), A057216, A057534, A057614.

Programs

Mathematica

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 *)

Formula

For n>15, a(n) = a(n-15). [Harvey P. Dale, May 02 2011]