A057216 To get next term, multiply by 17, add 1 and discard any prime factors < 17.

61, 173, 1471, 521, 4429, 4183, 2963, 257, 437, 743, 1579, 2237, 3803, 2309, 19627, 5561, 47269, 14881, 3833, 32581, 263, 43, 61, 173, 1471, 521, 4429, 4183, 2963, 257, 437, 743, 1579, 2237, 3803, 2309, 19627, 5561, 47269, 14881, 3833, 32581, 263, 43

Offset

0,1

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 22. - Alois P. Heinz, Jan 15 2021

Links

Table of n, a(n) for n=0..43.

Eric Weisstein's World of Mathematics, Collatz problem

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).

Example

61 -> 17*61+1 = 1038 = 2*3*173 -> 173, so second term is 173.

Mathematica

a[n_] := a[n] = Which[n == 0, 61, n <= 22, Times @@ Power @@@ Select[ FactorInteger[17 a[n - 1] + 1], #[[1]] >= 17&], True, a[n - 22]];
Table[a[n], {n, 0, 43}] (* Jean-François Alcover, Aug 21 2023 *)

Prog

(PARI) lista(nn) = {my(x=61); for (n=1, nn, print1(x, ", "); my(f=factor(17*x+1)); for (k=1, #f~, if (f[k, 1] < 17, f[k, 1] = 1)); x = factorback(f); ); } \\ Michel Marcus, Jan 19 2021

Crossrefs

Cf. A057446, A057522, A057534 (long version), A057614.

Sequence in context: A142482 A007488 A142538 * A139993 A088955 A087870

Adjacent sequences: A057213 A057214 A057215 * A057217 A057218 A057219

Keyword

nonn,easy

Author

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

Extensions

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

Status

approved