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 A330920 Number of steps required to reach 1 for repeated applications of the Collatz-inspired function f(n) = 6*n+5-(n mod 5), or -1 if 1 is never reached. 0
 0, 7, 5, 3, 1, 12, 31, 10, 29, 8, 27, 8, 8, 25, 6, 6, 23, 19, 19, 4, 21, 17, 17, 36, 2, 19, 15, 15, 34, 13, 129, 17, 13, 13, 32, 30, 32, 127, 15, 11, 11, 13, 144, 28, 30, 125, 13, 30, 13, 9, 11, 142, 26, 11, 28, 123, 11, 28, 11, 9, 140, 9, 140, 24, 9, 9, 28, 121 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Inspired by the Collatz conjecture, I tried to generalize for more divisors than 2. I quickly came up with a formula, and then discovered that Carnielliy had written about it previously in 2015. LINKS Carnielliy, Walter. Some Natural Generalizations Of The Collatz Problem, Applied Mathematics E-Notes, 2015, page 208. PROG (Python) def f(n, d):     """     A Collatz-like function.     When d == 2 this becomes '3x+1' problem exactly.     """     i = n % d     if r == 0:         return n / d     else:         # Produce a larger number that is divisible by d.         return (d + 1) * n + d - i def steps(n, d):     """     Return the number of steps needed to reach 1, or -1 if a 1 is never reached.     """     count = 0     seen = set([1])     x = n     # Loop until a cycle is detected.     while x not in seen:         seen.add(x)         x = f(x, d)         count += 1     if x == 1:         return count     else:         # There was a cycle         return -1 # Create a bunch of terms for d=5 S = [steps(x, d=5) for x in xrange(1, 1000)] print S CROSSREFS If you replace d=5 with d=2, this code produces A006577. Sequence in context: A085927 A180597 A219242 * A155816 A308414 A335985 Adjacent sequences:  A330917 A330918 A330919 * A330921 A330922 A330923 KEYWORD nonn AUTHOR Matt Donahoe, Aug 22 2020 STATUS approved

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Last modified December 5 06:51 EST 2020. Contains 338944 sequences. (Running on oeis4.)