A138751 revision #19
|
|
|
|
2, 7, 3, 17, 7, 29, 11, 41, 13, 17, 67, 79, 23, 89, 29, 29, 31, 127, 137, 37, 149, 163, 43, 47, 197, 53, 211, 59, 223, 59, 257, 67, 71, 281, 79, 307, 317, 331, 89, 89, 97, 367, 97, 389, 101, 401, 431, 449, 127, 461, 127, 127, 487, 127, 131, 137, 137, 547, 557, 149
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Composing the map A138750 with A007918 to the left and restricting it to the primes makes it a mapping from primes into primes which is a natural generalization of the Collatz problem to primes. (Looking at parity would not be interesting for primes, so using "mod 3" is the simplest nontrivial generalization.)
The only even prime p=2 is the only fixed point of this map and all odd primes seem to end up in the loop 7 -> 17 -> 11 -> 7, after a number of steps given in A138752.
The sequence A124123 lists the primes which do not occur in the present sequence.
See A138750 for further information.
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
a(1) = nextprime(2/2) = 2, a(2) = nextprime(2*3) = 7, a(3) = nextprime(5/2) = 7.
|
|
MATHEMATICA
|
|
|
PROG
|
(PARI) A138751(n) = { n=prime(n); nextprime( if( n%3==2, ceil(n/2), 2*n ))}
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
editing
|
|
|
|