A081849 -id:A081849 - cp's OEIS frontend

A081853 Consider recurrence b(0) = (2n+1)/2, b(n) = b(n-1)*ceiling(b(n-1)); sequence gives first integer reached.

3, 60, 14, 268065, 33, 2093, 60, 1204154941925628, 95, 13398, 138, 701600900, 189, 47415, 248, 1489788110004539889867929328515560588293, 315, 123728, 390, 34427225343, 473, 268065, 564, 19873182780430314444725, 663, 512298, 770, 467193780498, 885, 894443, 1008

Offset: 1

N. J. A. Sloane, Apr 13 2003

nonn

J. C. Lagarias and N. J. A. Sloane, Approximate squaring (pdf, ps), Experimental Math., 13 (2004), 113-128.

A001511 gives number of steps to reach an integer. Cf. A081849, A073524, A074078.

Cf. A081854.

a[n_]:=Module[{b=(2n+1)/2},While[!IntegerQ[b],b*=Ceiling[b]]; b]; Array[a,31] (* Stefano Spezia, Jun 26 2024 *)

Define F(x) = x(x+1)/2. Write 2n+1 = 2^i*m + 2^(i-1) + 1, then a(n) = (1/2)F^(i-1)(2n+1). E.g. n=4, 2n+1 = 9 = 2^4*0 + 2^3 + 1, so i=4, m=0 and F(F(F(9))) = F(F(45)) = F(1035) = 536130, a(4) = 536130/2 = 268065.

a(30)-a(31) from Stefano Spezia, Jun 26 2024

A081850 Consider recurrence b(0) = (2n+1)/4, b(n) = b(0)*ceiling(b(n-1)); sequence gives number of steps to reach an integer (or -1 if no integer is ever reached).

Original entry on oeis.org

3, 2, 3, 13, 1, 1, 4, 2, 2, 9, 2, 2, 1, 1, 7, 3, 7, 3, 4, 3, 1, 1, 2, 4, 5, 10, 5, 13, 1, 1, 14, 8, 5, 2, 10, 11, 1, 1, 6, 2, 2, 17, 2, 2, 1, 1, 3, 6, 16, 5, 3, 4, 1, 1, 2, 4, 7, 9, 4, 3, 1, 1, 15, 9, 4, 2, 7, 5, 1, 1, 3, 2, 2, 3, 2, 2, 1, 1, 5, 5, 6, 5, 6, 4, 1, 1, 2, 4, 4, 3, 3, 11, 1, 1, 3, 3, 7, 2, 4

Offset: 2

N. J. A. Sloane, Apr 13 2003

nonn

Robert Israel, Table of n, a(n) for n = 2..10000

Cf. A073524, A081849, A081851.

Digits := 100: c := ceil; A081850 := 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(t); fi; od; RETURN('FAIL'); end;

A081851 Consider recurrence b(0) = (2n+1)/4, b(n) = b(0)*ceiling(b(n-1)); sequence gives first integer reached (or -1 if no integer is ever reached).

Original entry on oeis.org

5, 7, 36, 1711985, 13, 15, 1700, 114, 168, 42000323, 275, 324, 58, 62, 23658393, 6055, 58311963, 9321, 121770, 13760, 135, 141, 1960, 344148, 5734229, 3391007266515, 8825709, 23546737390632357, 244, 252, 1526332099115586230, 105432399233, 27538521, 5680

Offset: 2

N. J. A. Sloane, Apr 13 2003

nonn

Robert Israel, Table of n, a(n) for n = 2..10000

Cf. A073524, A081849, A081850.

g:= proc(n) local b0, b, count;
  b0:= (2*n+1)/4; b:= b0;
  for count from 1 do
    b:= b0 * ceil(b);
    if b::integer then return b fi
  od
end proc:
map(g, [$2..100]); # Robert Israel, Sep 21 2018

A081852 Consider recurrence b(0) = n/3, b(n) = b(0)*ceiling(b(n-1)); sequence gives first integer reached (or -1 if no integer is ever reached).

Original entry on oeis.org

1, 4, 20, 2, 7, 8, 3, 26631380, 55, 4, 416, 112, 5, 32, 34, 6, 285, 13960, 7, 67358874, 214544, 8, 75, 78, 9, 62186796, 7399041846, 10, 1178, 173857344, 11, 136, 140, 12, 24494, 2090, 13, 78824360, 2624, 14, 215, 220, 15, 3772, 61617, 16, 23001295794169, 78900, 17, 312

Offset: 3

N. J. A. Sloane, Apr 13 2003

nonn

Cf. A073524, A081849, A081850, A081851. A074078 gives number of steps to reach an integer.

cp's OEIS Frontend

A081853 Consider recurrence b(0) = (2n+1)/2, b(n) = b(n-1)*ceiling(b(n-1)); sequence gives first integer reached.

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A081850 Consider recurrence b(0) = (2n+1)/4, b(n) = b(0)*ceiling(b(n-1)); sequence gives number of steps to reach an integer (or -1 if no integer is ever reached).

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A081851 Consider recurrence b(0) = (2n+1)/4, b(n) = b(0)*ceiling(b(n-1)); sequence gives first integer reached (or -1 if no integer is ever reached).

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Maple

A081852 Consider recurrence b(0) = n/3, b(n) = b(0)*ceiling(b(n-1)); sequence gives first integer reached (or -1 if no integer is ever reached).

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