A057534 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), a(n)/13 if 13|a(n), otherwise 17*a(n)+1.

61, 1038, 519, 173, 2942, 1471, 25008, 12504, 6252, 3126, 1563, 521, 8858, 4429, 75294, 37647, 12549, 4183, 71112, 35556, 17778, 8889, 2963, 50372, 25186, 12593, 1799, 257, 4370, 2185, 437, 7430, 3715, 743, 12632, 6316, 3158, 1579, 26844, 13422

Offset: 0

Author

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

Keywords

• nonn
• easy

Comments

This is the '17x+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 84. - Alois P. Heinz, Jan 19 2021

Links

• Ray Chandler, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Crossrefs

Cf. A057446, A057216 (short version), A057522, A057614.

Programs

Maple

with(numtheory): a := proc(n) option remember: local k; if n=0 then RETURN(61); fi: for k from 1 to 6 do if a(n-1) mod ithprime(k) = 0 then RETURN(a(n-1)/ithprime(k)); fi: od: RETURN(17*a(n-1)+1) end:

Mathematica

a[n_] := a[n] = Which[n == 0, 61, n <= 84, Module[{k}, For[k = 1, k < PrimePi[17], k++, If[Mod[a[n - 1], Prime[k]] == 0, Return[a[n - 1]/Prime[k]]]]; Return[17*a[n - 1] + 1]], True, a[n - 84]];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Aug 22 2023, after Maple code *)

PARI

a(n)=if(n, n=a(n-1); if(n%2, if(n%3, if(n%5, if(n%7, if(n%11, if(n%13, 17*n+1, n/13), n/11), n/7), n/5), n/3), n/2), 61) \\ Charles R Greathouse IV, Oct 13 2022

Extensions

More terms from James Sellers and Larry Reeves (larryr(AT)acm.org), Oct 18 2000