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

1,2

Links

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

Formula

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

Example

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).

Mathematica

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

Prog

(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

Crossrefs

Cf. A000217, A006577, A070975.

Sequence in context: A245736 A088660 A244263 * A020506 A193345 A197822

Adjacent sequences: A288020 A288021 A288022 * A288024 A288025 A288026

Keyword

nonn

Author

Ryan Pythagoras Newton Critchlow, Jun 04 2017

Status

approved