A057446 To get next term, multiply by 13, add 1 and discard any prime factors < 13.

73, 19, 31, 101, 73, 19, 31, 101, 73, 19, 31, 101, 73, 19, 31, 101, 73, 19, 31, 101, 73, 19, 31, 101, 73, 19, 31, 101, 73, 19, 31, 101, 73, 19, 31, 101, 73, 19, 31, 101, 73, 19, 31, 101, 73, 19, 31, 101, 73, 19, 31, 101, 73, 19, 31, 101, 73, 19, 31, 101

Offset: 0

Author

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

Keywords

• nonn
• easy

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.

Sequence has period 4. - Alois P. Heinz, Jan 19 2021

Examples

			73 -> 13*73+1 = 950 = 2*5^2*19 -> 19, so second term is 19.
		

Links

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

Crossrefs

Cf. A057216, A057522 (long version), A057534, A057614.

Programs

Mathematica

m13[n_]:=First[Times@@@Select[FactorInteger[13 n+1],#[[1]]>11&]]; NestList[ m13,73,80] (* or *) PadRight[{},80,{73,19,31,101}] (* Harvey P. Dale, Apr 16 2019 *)
a[n_] := a[n] = Which[n == 0, 73, n <= 4, Times @@ Power @@@ Select[ FactorInteger[13 a[n - 1] + 1], #[[1]] >= 13&], True, a[n - 4]];
Table[a[n], {n, 0, 59}] (* Jean-François Alcover, Aug 21 2023 *)