OFFSET
1,3
COMMENTS
LINKS
EXAMPLE
Starting from n = 27, the following is a shortest path leading to a value smaller than 27: 27 -> 82 -> 41 -> 124 -> 373 -> 1120 -> 560 -> 280 -> 140 -> 70 -> 35 -> 106 -> 53 -> 160 -> 80 -> 40 -> 20. It has 16 steps, thus a(27) = 16. Note the 3x+1 step from 124 to 373 which is not allowed in the ordinary Collatz problem.
PROG
(PARI) A290101(n) = { if(1==n, return(0)); my(S, k); S=[n]; k=0; while( S[1]>=n, k++; S=vecsort( concat(apply(x->3*x+1, S), apply(x->x\2, select(x->x%2==0, S) )), , 8); ); k } \\ After Max Alekseyev's code for A127885
(Python)
from sympy import flatten
def ok(n, L):
return any(i < n for i in L)
def a(n):
if n==1: return 0
L=[n]
i = 0
while not ok(n, L):
L=set(flatten([[3*k + 1, k//2] if k%2==0 else 3*k + 1 for k in L]))
i+=1
return i
print([a(n) for n in range(1, 121)]) # Indranil Ghosh, Aug 31 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Aug 20 2017
STATUS
approved