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A275663
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Number of squares in {n, f(n), f(f(n)), ...., 1}, where f is the Collatz function.
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1
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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
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1,3
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COMMENTS
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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).
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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]] (* Jean-François Alcover, Nov 17 2016, adapted from PARI *)
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PROG
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(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, ", "); ); ))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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