A193230 Start with 1; if even, divide by 2; if odd, add the next three primes.

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

Offset: 1

Author

N. J. A. Sloane, Jul 18 2011

Keywords

• nonn

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

Examples

			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)
		

Links

• 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).

Crossrefs

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

Programs

Mathematica

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

PARI

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