A280408 Irregular triangle read by rows listing the prime numbers that appear from the trajectory of n in Collatz Problem.

2, 2, 3, 5, 2, 2, 5, 2, 3, 5, 2, 7, 11, 17, 13, 5, 2, 2, 7, 11, 17, 13, 5, 2, 5, 2, 11, 17, 13, 5, 2, 3, 5, 2, 13, 5, 2, 7, 11, 17, 13, 5, 2, 23, 53, 5, 2, 2, 17, 13, 5, 2, 7, 11, 17, 13, 5, 2, 19, 29, 11, 17, 13, 5, 2, 5, 2, 2, 11, 17, 13, 5, 2, 23, 53, 5, 2, 3, 5, 2, 19, 29, 11, 17, 13, 5, 2

Offset

1,1

Links

Table of n, a(n) for n=1..87.

Example

The irregular array a(n,k) starts:
n\k   1   2   3   4   5   6
...
1:    2
2:    2
3:    3   5   2
4:    2
5:    5   2
6:    3   5   2
7:    7  11  17  13   5   2
8:    2
9:    7  11  17  13   5   2
10:   5  2
11:  11  17  13   5   2
12:   3   5   2
13:  13   5   2
14:   7  11  17  13   5   2
15:  23  53   5   2

Mathematica

Table[Select[NestWhileList[If[EvenQ@ #, #/2, 3 # + 1] &, n, # > 1 &], PrimeQ], {n, 2, 30}] // Flatten (* Michael De Vlieger, Jan 02 2017 *)

Prog

(Python)
from sympy import isprime
def a(n):
    if n==1: return [2]
    l=[n, ]
    while True:
        if n%2==0: n/=2
        else: n = 3*n + 1
        l+=[n, ]
        if n<2: break
    return list(filter(lambda i: isprime(i), l))
for n in range(1, 21): print a(n) # Indranil Ghosh, Apr 14 2017

Crossrefs

Cf. A070165, A280409.

Sequence in context: A329792 A058256 A140183 * A130725 A256015 A138117

Adjacent sequences: A280405 A280406 A280407 * A280409 A280410 A280411

Keyword

tabf,nonn

Author

Matthew Campbell, Jan 02 2017

Status

approved