A288023 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.

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

Offset: 1

Author

Ryan Pythagoras Newton Critchlow, Jun 04 2017

Keywords

• nonn

Examples

			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).
		

Links

• Ryan Pythagoras Newton Critchlow, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000217, A006577, A070975.

Programs

Mathematica

Table[Length[NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#>1&]]-1,{n,Accumulate[ Range[80]]}] (* Harvey P. Dale, Aug 17 2017 *)

Python

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

Formula

a(n) = A006577(A000217(n)). - Omar E. Pol, Jun 04 2017