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

0,1

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).

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 *)

Crossrefs

Cf. A057446, A057216, A057522, A057534.

Sequence in context: A369332 A022741 A225966 * A041548 A025931 A115234

Adjacent sequences: A057611 A057612 A057613 * A057615 A057616 A057617

Keyword

nonn,easy

Author

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

Status

approved