login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A193230 Start with 1; if even, divide by 2; if odd, add the next three primes. 6
1, 11, 60, 30, 15, 74, 37, 168, 84, 42, 21, 104, 52, 26, 13, 72, 36, 18, 9, 50, 25, 122, 61, 272, 136, 68, 34, 17, 88, 44, 22, 11, 60, 30, 15, 74, 37, 168, 84, 42, 21, 104, 52, 26, 13, 72, 36, 18, 9, 50, 25, 122, 61, 272, 136, 68, 34, 17, 88, 44, 22, 11, 60, 30, 15, 74, 37, 168, 84, 42, 21, 104, 52, 26, 13, 72, 36, 18, 9, 50, 25, 122, 61, 272, 136, 68, 34, 17, 88, 44, 22, 11, 60, 30, 15, 74, 37, 168, 84, 42, 21, 104 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Trajectory of 1 under the map x -> A174221(x).

Periodic with period of length 30, starting at a(2) = 11.

Angelini conjectures that the orbit under A174221 becomes periodic for any initial value. He calls this the PrimeLatz conjecture, as tribute to L. Collatz, known for the 3n+1 conjecture.

It has been checked that the loop (11, ..., 22) (or (9, ..., 18), to start with the smallest element) is the only loop (except for the fixed point 0) at least up to values not exceeding 10^8, and the orbit of every positive integer <= 10^4 does end in this loop. - M. F. Hasler, Oct 25 2017

It might have been more natural to start this sequence with offset 0. Since a(n) = a(n+30) from n = 2 on, this sequence consists essentially (except for the initial term) of the apparently unique "loop" of the "PrimeLatz" map A174221. It is used as such in related sequences A293978, ... - M. F. Hasler, Oct 31 2017

LINKS

Table of n, a(n) for n=1..102.

Eric Angelini, The PrimeLatz conjecture

E. Angelini, The PrimeLatz Conjecture [Cached copy, with permission]

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, 0, 0, 0, 0, 0, 0, 0, 0, 1).

EXAMPLE

1 is odd;  we add to 1 the next 3 primes (2,3,5) and get 11

11 is odd;  we get 11+(13+17+19)=60

60 is even; we get 30

30 is even; we get 15

15 is odd;  we get 15+(17+19+23)=74

74 is even; we get 37

37 is odd;  we get 37+(41+43+47)=168

168 is even; we get 84

84 is even; we get 42

42 is even; we get 21

21 is odd;  we get 21+(23+29+31)=104

104 is even; we get 52

52 is even; we get 26

26 is even; we get 13

13 is odd;  we get 13+(17+19+23)=72

72 is even; we get 36

36 is even; we get 18

18 is even; we get 9

9 is odd;  we get 9+(11+13+17)=50

50 is even; we get 25

25 is odd;  we get 25+(29+31+37)=122

122 is even; we get 61

61 is odd;  we get 61+(67+71+73)=272

272 is even; we get 136

136 is even; we get 68

68 is even; we get 34

34 is even; we get 17

17 is odd;  we get 17+(19+23+29)=88

88 is even; we get 44

44 is even; we get 22

22 is even; we get 11... thus entering in a loop.

...

(from Angelini's web page)

MATHEMATICA

NestList[If[EvenQ@ #, #/2, Total@ Prepend[NextPrime[#, {1, 2, 3}], #]] &, 1, 101] (* Michael De Vlieger, Oct 25 2017 *)

PROG

(PARI) vector(100, i, t=if(i>1, A174221(t), 1)) \\ M. F. Hasler, Oct 25 2017

CROSSREFS

Cf. A174221, A293980, A293979 (orbit of 83), A293978 (orbit of 443), A293981 (orbit of 209).

Sequence in context: A253207 A241860 A082884 * A077036 A076604 A076676

Adjacent sequences:  A193227 A193228 A193229 * A193231 A193232 A193233

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jul 18 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 11 01:18 EDT 2020. Contains 335600 sequences. (Running on oeis4.)