A057614 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), otherwise 11*a(n)+1.

17, 188, 94, 47, 518, 259, 37, 408, 204, 102, 51, 17, 188, 94, 47, 518, 259, 37, 408, 204, 102, 51, 17, 188, 94, 47, 518, 259, 37, 408, 204, 102, 51, 17, 188, 94, 47, 518, 259, 37, 408, 204, 102, 51, 17, 188, 94, 47, 518, 259, 37, 408, 204, 102, 51, 17, 188, 94, 47, 518, 259, 37, 408, 204, 102, 51

Offset: 0

Author

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

Keywords

• nonn
• easy

Comments

This is the '11x+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 11. - Alois P. Heinz, Jan 19 2021

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Collatz problem
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,1).

Crossrefs

Cf. A057446, A057216, A057522, A057534.

Programs

Mathematica

NestList[Which[Mod[#,2]==0,#/2,Mod[#,3]==0,#/3,Mod[#,5]==0,#/5,Mod[#,7]==0,#/7,True,11#+1]&,17,70] (* or *) PadRight[{},100,{17,188,94,47,518,259,37,408,204,102,51}] (* Harvey P. Dale, Jun 30 2025 *)