|
|
A368196
|
|
Irregular triangle read by rows where row n is the trajectory starting from n and ending with 2 of the map x -> A368241(x).
|
|
2
|
|
|
4, 6, 9, 13, 2, 5, 2, 6, 9, 13, 2, 7, 2, 8, 12, 17, 4, 6, 9, 13, 2, 9, 13, 2, 10, 14, 20, 28, 37, 6, 9, 13, 2, 11, 4, 6, 9, 13, 2, 12, 17, 4, 6, 9, 13, 2, 13, 2, 14, 20, 28, 37, 6, 9, 13, 2, 15, 21, 29, 6, 9, 13, 2, 16, 22, 30, 40, 52, 67, 6, 9, 13, 2, 17, 4, 6, 9, 13, 2
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
4,1
|
|
COMMENTS
|
It is conjectured that every starting n reaches 2 eventually. (If not then the sequence has an infinite final row.)
Map A368241(x) decreases to the prime gap x-prevprime(x) when x is prime, or increases to x+primepi(x) otherwise, and will reach 2 when x is the greater of a twin prime pair (A006512, preceding prime gap 2).
Prime gaps and x+primepi(x) may become large, but if the twin prime conjecture is true then there would be large twin primes they might reach too.
|
|
LINKS
|
|
|
FORMULA
|
T(n,0) = n.
T(n,k) = A368241(T(n,k-1)) for k >= 1.
|
|
EXAMPLE
|
Table T(n,k) begins:
n\k 0 1 2 3 4 5 6 7 8 9
--------------------------------------------
4: 4 6 9 13 2
5: 5 2
6: 6 9 13 2
7: 7 2
8: 8 12 17 4 6 9 13 2
9: 9 13 2
10: 10 14 20 28 37 6 9 13 2
11: 11 4 6 9 13 2
12: 12 17 4 6 9 13 2
13: 13 2
14: 14 20 28 37 6 9 13 2
15: 15 21 29 6 9 13 2
16: 16 22 30 40 52 67 6 9 13 2
17: 17 4 6 9 13 2
18: 18 25 34 45 59 6 9 13 2
19: 19 2
20: 20 28 37 6 9 13 2
|
|
PROG
|
(PARI) row(n) = my(list=List(n)); while(n!=2, n = if (isprime(n), n - precprime(n-1), n + primepi(n)); listput(list, n)); Vec(list); \\ Michel Marcus, Dec 17 2023
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,tabf
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|