A361733 Length of the Collatz (3x + 1) trajectory from k = 10^n - 1 to a term less than k, or -1 if the trajectory never goes below k.
4, 7, 17, 12, 113, 17, 79, 22, 51, 33, 64, 35, 128, 56, 110, 53, 84, 128, 107, 115, 175, 82, 477, 172, 141, 182, 188, 110, 159, 167, 301, 206, 151, 146, 128, 195, 190, 299, 208, 276, 180, 185, 500, 203, 229, 190, 265, 270, 288, 252, 299, 208, 350, 348, 459, 330, 314, 268, 490, 361, 578
Offset: 1
Keywords
Examples
a(1) = 4 as for k = 9, the Collatz trajectory begins 9, 28, 14, 7, ...; a(2) = 7 as for k = 99, the Collatz trajectory begins 99, 298, 149, 448, 224, 112, 56, ...; a(3) = 17 as for k = 999, the Collatz trajectory begins 999, 2998, 1499, 4498, 2249, 6748, 3374, 1687, 5062, 2531, 7594, 3797, 11392, 5696, 2848, 1424, 712, ... .
Programs
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Mathematica
collatzLen[a_Integer] := Module[{len = 1, x = a}, While[x >= a, If[Mod[x, 2] > 0, x = 3 x + 1, x = Quotient[x, 2] ]; len++ ]; Return[len] ] -
PARI
f(n) = if (n%2, 3*n+1, n/2); \\ A006370 b(n) = if (n<3, return(n)); my(m=n, nb=0); while (1, m = f(m); nb++; if (m < n, return(nb+1));); \\ A074473 a(n) = b(10^n-1); \\ Michel Marcus, Mar 28 2023
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Python
def collatz_len(a): length = 1 x = a while x >= a: if x % 2 > 0: x = 3 * x + 1 else: x = x // 2 length += 1 return length
Formula
a(n) = A074473(10^n-1).
Comments