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A198584 Odd numbers producing 3 odd numbers in the Collatz (3x+1) iteration. 14
3, 13, 53, 113, 213, 227, 453, 853, 909, 1813, 3413, 3637, 7253, 7281, 13653, 14549, 14563, 29013, 29125, 54613, 58197, 58253, 116053, 116501, 218453, 232789, 233013, 464213, 466005, 466033, 873813, 931157, 932053, 932067, 1856853, 1864021, 1864133 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

One of the odd numbers is always 1. So besides a(n), there is one other odd number, A198585(n), which is a term in A002450.

Sequences A228871 and A228872 show that there are two sequences here: the odd numbers in order and out of order. - T. D. Noe, Sep 12 2013

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1009

EXAMPLE

The Collatz iteration of 113 is 113, 340, 170, 85, 256, 128, 64, 32, 16, 8, 4, 2, 1, which shows that 113, 85, and 1 are the three odd terms.

MATHEMATICA

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; t = {}; Do[If[Length[Select[Collatz[n], OddQ]] == 3, AppendTo[t, n]], {n, 1, 10000, 2}]; t

PROG

(Python)

# get n-th term in sequence

def isqrt(n):

  i=0

  while(i*i<=n):

    i+=1

  return i-1

for n in range (200):

  s = isqrt(3*n)//3

  a = s*3

  b = (a*a)//3

  c = n-b

  d = 4*(n*3+a+(c<s)+(c>4*s+1)+(c>5*s+1))+5

  e = isqrt(d)

  f = e-1-( (d-e*e) >> 1 )

  r = ((((8<<e)-(1<<f))//3)-1)//3

  print(r, end =", ") # André Hallqvist, Jul 25 2019

(Python)

# just prints the sequence

for a in range (5, 100, 1):

  for b in range(a-8+4*(a&1), 0, -6):

    print(( ((1<<a)-(1<<b))//3-1)//3 , end=", ") # André Hallqvist, Aug 14 2019

CROSSREFS

Cf. A062053 (numbers producing 3 odds in their Collatz iteration).

Cf. A092893 (least number producing n odd numbers).

Cf. A198586-A198593 (odd numbers producing 2-10 odd numbers).

Cf. A228871, A228872.

Sequence in context: A063682 A082376 A065059 * A342815 A072197 A065838

Adjacent sequences:  A198581 A198582 A198583 * A198585 A198586 A198587

KEYWORD

nonn

AUTHOR

T. D. Noe, Oct 28 2011

STATUS

approved

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Last modified May 8 15:40 EDT 2021. Contains 343666 sequences. (Running on oeis4.)