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

%I A280408 #28 Jun 07 2025 11:56:52
%S A280408 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,
%T A280408 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,
%U A280408 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
%N A280408 Irregular triangle read by rows listing the prime numbers that appear from the trajectory of n in Collatz Problem.
%H A280408 David Radcliffe, <a href="/A280408/b280408.txt">Table of n, a(n) for n = 1..10000</a>
%e A280408 The irregular array a(n,k) starts:
%e A280408 n\k   1   2   3   4   5   6
%e A280408 ...
%e A280408 1:    2
%e A280408 2:    2
%e A280408 3:    3   5   2
%e A280408 4:    2
%e A280408 5:    5   2
%e A280408 6:    3   5   2
%e A280408 7:    7  11  17  13   5   2
%e A280408 8:    2
%e A280408 9:    7  11  17  13   5   2
%e A280408 10:   5  2
%e A280408 11:  11  17  13   5   2
%e A280408 12:   3   5   2
%e A280408 13:  13   5   2
%e A280408 14:   7  11  17  13   5   2
%e A280408 15:  23  53   5   2
%t A280408 Table[Select[NestWhileList[If[EvenQ@ #, #/2, 3 # + 1] &, n, # > 1 &], PrimeQ], {n, 2, 30}] // Flatten (* _Michael De Vlieger_, Jan 02 2017 *)
%o A280408 (Python)
%o A280408 from sympy import isprime
%o A280408 def a(n):
%o A280408     if n==1: return [2]
%o A280408     l=[n, ]
%o A280408     while True:
%o A280408         if n%2==0: n//=2
%o A280408         else: n = 3*n + 1
%o A280408         l+=[n, ]
%o A280408         if n<2: break
%o A280408     return list(filter(lambda i: isprime(i), l))
%o A280408 for n in range(1, 21): print(a(n)) # _Indranil Ghosh_, Apr 14 2017
%Y A280408 Cf. A070165, A280409.
%K A280408 tabf,nonn
%O A280408 1,1
%A A280408 _Matthew Campbell_, Jan 02 2017