cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 11-14 of 14 results.

A057686 Trajectory of 23 under the `23x+1' map.

Original entry on oeis.org

23, 530, 265, 53, 1220, 610, 305, 61, 1404, 702, 351, 117, 39, 13, 1, 24, 12, 6, 3, 1, 24, 12, 6, 3, 1, 24, 12, 6, 3, 1, 24, 12, 6, 3, 1, 24, 12, 6, 3, 1, 24, 12, 6, 3, 1, 24, 12, 6, 3, 1, 24, 12, 6, 3, 1, 24, 12, 6, 3, 1, 24, 12, 6, 3, 1, 24, 12, 6, 3, 1
Offset: 0

Views

Author

N. J. A. Sloane, Oct 20 2000

Keywords

Comments

See A057684 for definition.

Links

Crossrefs

Cf. A057446, A057216, A057522, A057534, A057614.
See also A033478, A057688, A057684, A057685, A057686, A057687, A057689, A057690, A057691.

Programs

  • Mathematica
    Px1[p_,n_]:=Catch[For[i=1,iPaolo Xausa, Dec 10 2023 *)

A057687 Trajectory of 29 under the `29x+1' map.

Original entry on oeis.org

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
Offset: 0

Views

Author

N. J. A. Sloane, Oct 20 2000

Keywords

Comments

See A057684 for definition.

Links

Crossrefs

Cf. A057446, A057216, A057522, A057534, A057614. See also A033478, A057688, A057684, A057685, A057686, A057687, A057689, A057690, A057691.

Programs

  • Mathematica
    Px1[p_,n_]:=Catch[For[i=1,iPaolo Xausa, Dec 10 2023 *)

A058047 Generalized Collatz sequences: primes resulting in a cycle containing 1.

Original entry on oeis.org

3, 5, 7, 29, 41, 79
Offset: 0

Views

Author

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

Keywords

Comments

For each prime P check the generalized Collatz sequence of each integer N > 1 defined by c(1) = N, c(n+1) = c(n) * P + 1 if F > P, otherwise c(n+1) = c(n) / F, where F is the smallest factor of c(n), until c(n) = c(m) for n > m starts a cycle. If all c(i) > 1, then P does not belong to the sequence (and vice versa).
All terms are as yet only conjectures. Jeff Heleen checked the primes < 1000 and start points up to 10000000 (see Prime Puzzle 114 and example below). a(1)=3 is the ordinary Collatz problem. - Frank Ellermann, Jan 20 2002
The jOEIS program uses start points up to 10^8 and yields [3, 5, 7, 19, 29, 41, 43*, 53, 71*, 79, 89*, 103*, 107, 109*, 127, 131*, 137] followed by [139, 149, 157, 179, 191, 197, 199, 211, 227, ...]. The terms in the first list without asterisks agree with A106919. - Georg Fischer, Jun 17 2023

Examples

			a(4) > 11, e.g.: 17, 17*11 + 1 = 188, 188/(2*2) = 47, 47*11 + 1 = 518, 518/(2*7) = 37, 37*11 + 1 = 408, 408/(2*2*2*3) = 17 (cycle without 1).
For p = 29 e.g.: 17, 17*29 + 1 = 494, 494/(2*13*19) = 1, 1*29 + 1 = 30, 30/30 = 1 (cycle with 1), no counterexample below 10000000.

Links

Crossrefs

Cf. A057216, A057446, A057534, A057614, A058048, A106919.

Programs

  • Java
    Cf. link to the program in the jOEIS project.

Extensions

Edited by Frank Ellermann, Jan 20 2002

A058048 For each prime P consider the generalized Collatz sequence of each integer N > 1 defined by c(0) = N, c(m+1) = c(m) * P + 1 if F > P, else c(m+1) = c(m) / F, where F is the smallest factor of c(m), until the sequence cycles. If all c(i) > 1 for some starting number N then P belongs to the sequence (and vice versa).

Original entry on oeis.org

2, 11, 13, 17, 19, 23, 31, 37, 43, 47, 53, 59, 61, 67, 71, 73, 83, 97, 101, 103, 113, 131, 137, 139, 151, 163, 167, 173, 181, 193, 197, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 313, 331, 347, 353, 367, 373, 379, 383, 389, 401
Offset: 1

Views

Author

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

Keywords

Comments

Missing primes are as yet only conjectures. Jeff Heleen checked the primes < 1000 and start points up to 10000000 (see Prime Puzzle 114 and example below). P=3 is the ordinary Collatz problem.

Examples

			With P=11 and c(0)=17 then {c(m)} is 17, 188, 94, 47, 518, 37, 408, 68, 34, 17, ...

Links

Crossrefs

Prime complement of A058047. Cf. A057446, A057216, A057534, A057614, A058047.

Extensions

Edited by Henry Bottomley, Jun 14 2002
Corrected by T. D. Noe, Oct 25 2006
Previous Showing 11-14 of 14 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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