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

Author

Matthew Campbell, Jan 02 2017

Keywords

• tabf
• nonn

Examples

			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
		

Links

• David Radcliffe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A070165, A280409.

Programs

Mathematica

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

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