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A275866
Number of semiprimes in {n, f(n), f(f(n)), ...., 1}, where f is the Collatz function.
3
0, 0, 2, 1, 1, 3, 5, 1, 7, 2, 4, 3, 2, 6, 6, 1, 3, 7, 6, 2, 2, 5, 4, 3, 8, 3, 38, 6, 5, 6, 36, 1, 9, 4, 4, 7, 6, 7, 12, 2, 37, 2, 9, 5, 4, 5, 35, 3, 8, 8, 8, 3, 2, 38, 38, 6, 11, 6, 10, 6, 5, 37, 36, 1, 9, 9, 8, 4, 4, 4, 34, 7, 38, 7, 3, 7, 7, 12, 11, 2, 6, 38
OFFSET
1,3
COMMENTS
Number of semiprimes in the trajectory of n under the 3x+1 map (i.e. the number of semiprimes until the trajectory reaches 1).
It seems that about 15% of the terms satisfy a(i) = a(i+1). For example, up to 100000, 15140 terms satisfy this condition.
LINKS
EXAMPLE
a(9)=7 because the trajectory of 9 is 9 -> 28 -> 14 -> 7 -> 22 -> 11 -> 34 -> 17 -> 52 -> 26 -> 13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1 and the 7 semiprimes of this trajectory are 9, 14, 22, 34, 26, 10 and 4.
MATHEMATICA
Table[Count[NestWhileList[If[EvenQ@ #, #/2, 3 # + 1] &, n, # != 1 &], k_ /; PrimeOmega@ k == 2], {n, 82}] (* Michael De Vlieger, Aug 11 2016 *)
PROG
(PARI) print1(0, ", "); for(n=2, 100, s=n; t=0; while(s!=1, if(bigomega(s)==2 , t=t+1, t=t); if(s%2==0, s=s/2, s=(3*s+1)); if(s==1, print1(t", "))))
CROSSREFS
Sequence in context: A230698 A090234 A286380 * A007754 A144866 A058732
KEYWORD
nonn
AUTHOR
Michel Lagneau, Aug 11 2016
STATUS
approved