A133423 -id:A133423 - cp's OEIS frontend

A133424 Analog of A060410 for the 5x+1 problem (cf. A133419).

6, 66, 216, 366, 516, 666, 816, 1116, 2016, 4866, 5766, 8616, 9516, 229866, 286116, 473616, 737016, 3230766, 4438266, 6260016, 10637016, 107662496, 117661116, 152291166, 176254866, 179900766, 201566166, 230949516

Offset: 1

N. J. A. Sloane, Nov 27 2007

nonn

The 5x+1 map sends x to x/2 if x is even, x/3 if x is divisible by 3, otherwise 5x+1.

N. J. A. Sloane, Table of n, a(n) for n=1..89 (from the web page of Tomás Oliveira e Silva)
Tomás Oliveira e Silva, The px+1 problem
Index entries for sequences related to 3x+1 (or Collatz) problem

Cf. A133419, A133423, A133419, ...

A270968 Reduced 5x+1 function R applied to the odd integers: a(n) = R(2n-1), where R(k) = (5k+1)/2^r, with r as large as possible.

Original entry on oeis.org

3, 1, 13, 9, 23, 7, 33, 19, 43, 3, 53, 29, 63, 17, 73, 39, 83, 11, 93, 49, 103, 27, 113, 59, 123, 1, 133, 69, 143, 37, 153, 79, 163, 21, 173, 89, 183, 47, 193, 99, 203, 13, 213, 109, 223, 57, 233, 119, 243, 31, 253, 129, 263, 67, 273, 139, 283, 9, 293, 149, 303

Offset: 1

Michel Lagneau, Mar 27 2016

The odd-indexed terms a(2i+1) = 10i+3 = A017305(i), i>=0;
a(4i+4) = 10i+9 = A017377(i), i>=0;
a(8i+6) = 10i+7 = A017353(i), i>=0;
a(16i+2) = 10i+1 = A017281(i), i>=0.
Note that a(n) = a(16n-6) = a(6n-2)/3. No multiple of 5 is in this sequence.
a(n) = R(2n-1) < 2n-1 for n = 2, 6, 10, ..., 2+4i,...

			a(4)=9 because (2*4-1) = 7  -> (5*7+1)/2^2 = 9.

Cf. A075677, A017281, A017305, A017353, A017377, A133423, A133424, A174795, A133419, A133420, A232711, A259207, A267969.

nextOddK[n_] := Module[{m=5n+1}, While[EvenQ[m], m=m/2]; m]; (* assumes odd n *) Table[nextOddK[n], {n, 1, 200, 2}]

a(n) = my(m = 2*n-1, c = 5*m+1); c/2^valuation(c, 2); \\ Michel Marcus, Mar 27 2016

a(n) = A000265(A017341(n-1)). - Michel Marcus, Mar 27 2016

cp's OEIS Frontend

A133424 Analog of A060410 for the 5x+1 problem (cf. A133419).

Views

Author

Keywords

Comments

Links

Crossrefs

A270968 Reduced 5x+1 function R applied to the odd integers: a(n) = R(2n-1), where R(k) = (5k+1)/2^r, with r as large as possible.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

PARI

Formula