A211346 a(1) = 1; for n>1, let k = n-1 mod 4, then a(n) = operation k applied to the pair (a(n-1), n), where operation 1 is addition, operation 2 is difference (with reset to n if 0), operation 3 is multiplication and operation 0 is division with rounding.

1, 3, 3, 12, 2, 8, 1, 8, 1, 11, 11, 132, 10, 24, 9, 144, 8, 26, 7, 140, 7, 29, 6, 144, 6, 32, 5, 140, 5, 35, 4, 128, 4, 38, 3, 108, 3, 41, 2, 80, 2, 44, 1, 44, 1, 47, 47, 2256, 46, 96, 45, 2340, 44, 98, 43, 2408, 42, 100, 41, 2460, 40, 102, 39, 2496, 38, 104

Offset

1,2

Comments

After n=1, the values of n where a(n)=1 occur in pairs: 7, 9; 43, 45; 207, 209; 943, 945; 4255, 4257; 19159, 19161; 86227,86229; 388035, 388037; 1746171, 1746173; 7857783, 7857785; 35360035, 35360037; etc. [edited by Jon E. Schoenfield, Dec 11 2014]

This occurs only when avoiding zeros and negative numbers form operations and also with four operation sequences [+, -, *, /]; [-, *, /, +]; [*, /, +, -] & [/, +, -, *] among total 24 permutation ones.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..5000

Kival Ngaokrajang, Scatter plot in log-log scale for n = 1..10^5, Centipede-like pattern.

Formula

a(1) = 1, for n >= 2; if (n - (4 * (round(n/4) - 1)) = 2, a(n) = a(n - 1) + n; if (n - (4 * (round(n/4) - 1)) = 3, a(n) = abs(a(n - 1) - n), if a(n - 1) = n, a(n) = n; if (n - (4 * (round(n/4) - 1)) = 4, a(n) = a(n-1) * n; if (n - (4 * (round(n/4) - 1)) = 5, a(n) = round(a(n - 1) / n).

Example

a(2) = a(1) + 2 = 3
a(3) = a(2) - 3 = 0, a(3) = n = 3
a(4) = a(3) * 4 = 12
a(5) = a(4) / 5 = round(12/5) = 2
a(6) = a(5) + 6 = 8,...

Maple

a:= proc(n) option remember; `if`(n<2, n,
       [(x, y)->round(x/y), (x, y)->x+y,
        (x, y)->`if`(x-y=0, y, abs(x-y)), (x, y)->x*y]
       [1+irem(n-1, 4)](a(n-1), n))
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Feb 17 2013

Mathematica

a[n_] := a[n] = If[n==1, 1, With[{k = Mod[n, 4]}, Switch[k, 0, a[n-1] n, 1, Round[a[n-1]/n], 2, a[n-1]+n, 3, If[a[n-1]==n, n, Abs[a[n-1]-n]]]]];
Array[a, 100] (* Jean-François Alcover, Mar 15 2021 *)

Prog

(Small Basic)
a[1]=1
For n=2 To 100
  nn = math.Remainder(n, 4)
  If nn = 2 Then ' operation +
    a[n]=a[n-1]+n
  Else
  EndIf
  If nn = 3 Then ' operation -
    If a[n-1] = n Then
      a[n]=n
      Goto OUT
    Else
    EndIf
    a[n]=Math.Abs(a[n-1]-n)
  Else
  EndIf
  OUT:
  If nn=0 Then ' operation *
    a[n]=a[n-1]*n
  Else
  EndIf
  If nn=1 Then ' operation  /
    a[n]=math.Round(a[n-1]/n)
  Else
EndIf
EndFor
For j = 1 to 100
  TextWindow.Write(j+" ")
  TextWindow.Write(a[j])
  TextWindow.WriteLine(" ")
EndFor

Crossrefs

Sequence in context: A352582 A078225 A244247 * A163372 A349922 A066437

Adjacent sequences: A211343 A211344 A211345 * A211347 A211348 A211349

Keyword

nonn,look

Author

Kival Ngaokrajang, Feb 05 2013

Status

approved