

A275663


Number of squares in {n, f(n), f(f(n)), ...., 1}, where f is the Collatz function.


1



1, 1, 3, 2, 3, 3, 3, 2, 4, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 4, 3, 3, 3, 4, 3, 5, 3, 3, 3, 5, 3, 5, 3, 3, 5, 3, 3, 3, 3, 5, 4, 5, 3, 3, 3, 5, 3, 4, 4, 3, 3, 3, 5, 5, 3, 5, 3, 3, 3, 3, 5, 3, 4, 5, 5, 3, 3, 3, 3, 5, 5, 5, 3, 5, 3, 3, 3, 3, 3, 4, 5, 5, 4, 5, 5, 3
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OFFSET

1,3


COMMENTS

Or number of squares in the trajectory of n under the 3x+1 map (i.e. the number of squares until the trajectory reaches 1).


LINKS



EXAMPLE

The finite sequence n, f(n), f(f(n)), ...., 1 for n = 12 is: 12, 6, 3, 10, 5, 16, 8, 4, 2, 1, which has three square terms. Hence a(12) = 3.


MATHEMATICA

Reap[For[n=1, n <= 100, n++, s=n; t=1; While[s != 1, If[IntegerQ[Sqrt[s]], t++]; If[EvenQ[s], s=s/2, s=3*s+1]]; If[s == 1, Sow[t]]]][[2, 1]] (* JeanFrançois Alcover, Nov 17 2016, adapted from PARI *)


PROG

(PARI) print1(1, ", "); for(n=2, 100, s=n; t=1; while(s!=1, if(issquare(s), t++, t=t); if(s%2==0, s=s/2, s=(3*s+1)); if(s==1, print1(t, ", "); ); ))


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



