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A288023
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Number of steps to reach 1 in the Collatz 3x+1 problem starting with the n-th triangular number, or -1 if 1 is never reached.
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1
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0, 7, 8, 6, 17, 7, 18, 21, 16, 112, 27, 35, 92, 38, 20, 15, 36, 124, 106, 39, 127, 109, 16, 16, 24, 81, 107, 40, 27, 35, 110, 30, 43, 74, 38, 113, 170, 46, 121, 28, 103, 116, 36, 98, 124, 137, 18, 119, 132, 83, 26, 127, 26, 47, 34, 122, 91, 148, 117, 130, 37, 37, 112, 32, 76, 94, 58, 120, 120, 89, 133, 53, 115, 66
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OFFSET
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1,2
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LINKS
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FORMULA
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EXAMPLE
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For n = 2, the 2nd triangular number is 3, which takes 7 steps to reach 1 in the Collatz (3x+1) problem: (10, 5, 16, 8, 4, 2, 1).
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MATHEMATICA
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Table[Length[NestWhileList[If[EvenQ[#], #/2, 3#+1]&, n, #>1&]]-1, {n, Accumulate[ Range[80]]}] (* Harvey P. Dale, Aug 17 2017 *)
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PROG
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(Python 3)
num = 1
def triangleN(x):
return x*(x+1)/2
def stepCount(x):
x = int(x)
steps = 0
while True:
if x == 1:
break
elif x % 2 == 0:
x = x/2
steps += 1
else:
x = x*3 + 1
steps += 1
return steps
while True:
print(stepCount(triangleN(num)))
num += 1
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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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