A057687 Trajectory of 29 under the `29x+1' map: x -> x/p if p = least prime factor(x) < 29, else x*29 + 1.

29, 842, 421, 12210, 6105, 2035, 407, 37, 1074, 537, 179, 5192, 2596, 1298, 649, 59, 1712, 856, 428, 214, 107, 3104, 1552, 776, 388, 194, 97, 2814, 1407, 469, 67, 1944, 972, 486, 243, 81, 27, 9, 3, 1, 30, 15, 5, 1, 30, 15, 5, 1, 30, 15, 5, 1, 30, 15, 5, 1, 30, 15, 5, 1

Offset

0,1

Comments

See A057684 for definition.

Links

Table of n, a(n) for n=0..59.

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

Formula

a(n) = a(n - 4) for n > 42. - M. F. Hasler, Feb 11 2026

Example

29 (prime) -> 29*29+1 = 842 (even) -> 842/2 = 421 (prime) => 421*29+1 = 12210 (even) -> 12210/2 = 6105 (multiple of 3) -> 6105/3 = 2035 -> 2035/5 = 407 -> 407/11 = 37 -> 37*29+1 = 1074 -> ...

Mathematica

Module[{lpf}, NestList[If[1 < (lpf = FactorInteger[#][[1, 1]]) < 29, #/lpf, #*29 + 1] &, 29, 100]] (* Paolo Xausa, Feb 13 2026 *)

Crossrefs

Cf. A033478 (similar for 3), A057688 (for 5), A057684 (for 13), A057685 (for 19), A057686 (for 23).

Cf. A057689, A057690, A057691 (maximum, cycle and transition length for Px+1).

See also A057614, A057522, A057446, A057216, A057534 (trajectories under 11x+1, 13x+1 and 17x+1).

Cf. A020639 (least prime factor).

Sequence in context: A262337 A009973 A278475 * A049667 A042626 A157877

Adjacent sequences: A057684 A057685 A057686 * A057688 A057689 A057690

Keyword

nonn,easy

Author

N. J. A. Sloane, Oct 20 2000

Extensions

Edited by M. F. Hasler, Feb 11 2026

Status

approved