This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a(1)=7 as the first Mersenne prime is 3. So starting at 3 the steps are 10, 5, 16, 8, 4, 2, 1.
collatz[k_] := (If[OddQ[k], j=3k+1, j=k/2]; j); step[m_] := (p=1; n=m; While[n!=1, (n=collatz[n]; p++)]; p-1); list = {2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951}; Table[step[2^s-1], {s,list}] (* warning: the list should be limited so as to run in a reasonable amount of time *)
\\ See Raab link. \\ Martin Raab, May 11 2023
a(1) = {c(1) = prime(1) = 2, 2 mod 2 = 0, c(2) = 2/2 = 1, z=2} = 2;
a(3) = {c(1) = prime(3) = 5, 5 mod 2 = 1, c(2) = 3*5 + 1 = 16; 16 mod 2 = 0, c(3) = 16/2 = 8; 8 mod 2 = 0, c(4) = 8/2 = 4; 4 mod 2 = 0, c(5) = 4/2 = 2; 2 mod 2 = 0, c(6) = 2/2 = 1, z=6} = 6.
a(n)=n=prime(n);A=List;while(n != 1,listput(A,n);if(n%2==0,n=n/2,n=3*n+1));listput(A,1);return(#Vec(A)) \\ Edward Jiang, Sep 06 2014
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).
Table[Length[NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#>1&]]-1,{n,Accumulate[ Range[80]]}] (* Harvey P. Dale, Aug 17 2017 *)
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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