%I #22 Dec 07 2019 12:18:28
%S 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 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 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 Irregular triangle read by rows listing the prime numbers that appear from the trajectory of n in Collatz Problem.
%e The irregular array a(n,k) starts:
%e n\k 1 2 3 4 5 6
%e ...
%e 1: 2
%e 2: 2
%e 3: 3 5 2
%e 4: 2
%e 5: 5 2
%e 6: 3 5 2
%e 7: 7 11 17 13 5 2
%e 8: 2
%e 9: 7 11 17 13 5 2
%e 10: 5 2
%e 11: 11 17 13 5 2
%e 12: 3 5 2
%e 13: 13 5 2
%e 14: 7 11 17 13 5 2
%e 15: 23 53 5 2
%t Table[Select[NestWhileList[If[EvenQ@ #, #/2, 3 # + 1] &, n, # > 1 &], PrimeQ], {n, 2, 30}] // Flatten (* _Michael De Vlieger_, Jan 02 2017 *)
%o (Python)
%o from sympy import isprime
%o def a(n):
%o if n==1: return [2]
%o l=[n, ]
%o while True:
%o if n%2==0: n/=2
%o else: n = 3*n + 1
%o l+=[n, ]
%o if n<2: break
%o return list(filter(lambda i: isprime(i), l))
%o for n in range(1, 21): print a(n) # _Indranil Ghosh_, Apr 14 2017
%Y Cf. A070165, A280409.
%K tabf,nonn
%O 1,1
%A _Matthew Campbell_, Jan 02 2017
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