A081849 Consider recurrence b(0) = (2n+1)/2, b(n) = b(0)*ceiling(b(n-1)); sequence gives first integer reached.

3, 20, 14, 468, 33, 299, 60, 47328, 95, 1218, 138, 25475, 189, 3161, 248, 20830128, 315, 6512, 390, 181138, 473, 11655, 564, 9015167, 663, 18974, 770, 671745, 885, 28853, 1008, 38906570560, 1139, 41676, 1278, 1799888, 1425, 57827, 1580, 110341278, 1743, 77690

Offset

1,1

Comments

k = A001511(n) is the number of steps to reach an integer b(k).

Links

Table of n, a(n) for n=1..42.

Formula

a(n) = s*(n*s^k - 1/2) / (s-1) where s = b(0) = (2*n+1)/2 and k = A001511(n). - Kevin Ryde, Jun 30 2024

Maple

Digits := 100: c := ceil; A081849 := proc(a) local i, t0, t; t0 := a; t := 0; for i from 1 to 100 do if whattype(t0) <> integer then t0 := a*c(t0); t := t+1; else RETURN(t0); fi; od; RETURN('FAIL'); end;

Mathematica

a[n_]:=Module[{b=b0=(2n+1)/2}, While[!IntegerQ[b], b=b0*Ceiling[b]]; b]; Array[a, 42] (* Stefano Spezia, Jun 26 2024 *)

Prog

(Python)
from math import ceil
from fractions import Fraction
def a(n):
  b0 = b = Fraction((2*n+1), 2)
  while b.denominator != 1: b = b0*ceil(b)
  return b.numerator
print([a(n) for n in range(1, 43)]) # Michael S. Branicky, Mar 20 2021
(PARI) a(n) = if(n==1, 3, my(t=2*n+1, k=1+valuation(n, 2)); n*t^(k+1) >>k \ (t-2)); \\ Kevin Ryde, Jun 30 2024

Crossrefs

Cf. A001511, A081853, A073524, A074078.

Sequence in context: A126810 A115280 A212995 * A333667 A375618 A169642

Adjacent sequences: A081846 A081847 A081848 * A081850 A081851 A081852

Keyword

nonn,easy

Author

N. J. A. Sloane, Apr 13 2003

Status

approved