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

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 22. - Alois P. Heinz, Jan 15 2021

Examples

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

Links

• 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).

Crossrefs

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

Programs

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 *)

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

Extensions

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