cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A317854 Let b(1) = b(2) = 1; for n >= 3, b(n) = n - b(t(n)) - b(n-t(n)) where t = A287422. a(n) = 2*b(n) - n.

Original entry on oeis.org

1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, -2, -1, 0, -1, 0, 1, 0, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 0, 1, 0, -1, 0, -1, -2, -3, -4, -3, -2, -1, -2, -3, -2, -3, -4, -5, -6, -5, -4, -3, -2, -3, -2, -1, -2, -3, -4, -3, -2, -1, 0, -1, 0, 1, 0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 4, 5
Offset: 1

Views

Author

Altug Alkan, Aug 09 2018

Keywords

Comments

A different version of A317742. Similar to A317754.

Links

Crossrefs

Cf. A287422, A317742, A317754.

Programs

  • Maple
    t:= proc(n) option remember; `if`(n<3, 1,
      n -t(t(n-1)) -t(n-t(n-1)))
    end:
b:= proc(n) option remember; `if`(n<3, 1,
      n -b(t(n)) -b(n-t(n)))
    end:
seq(2*b(n)-n, n=1..100); # after Alois P. Heinz at A317686
  • Mathematica
    t[1]=t[2]=1; t[n_] := t[n] = n - t[t[n-1]] - t[n - t[n-1]]; b[1]=b[2]=1; b[n_] := b[n] = n - b[t[n]] - b[n - t[n]]; a[n_] := 2*b[n] - n; Array[a, 95] (* Giovanni Resta, Aug 14 2018 *)
  • PARI
    t=vector(99); t[1]=t[2]=1; for(n=3, #t, t[n] = n-t[n-t[n-1]]-t[t[n-1]]); b=vector(99); b[1]=b[2]=1; for(n=3, #b, b[n] = n-b[t[n]]-b[n-t[n]]); vector(99, k, 2*b[k]-k)
(C++) See Links section.

Formula

abs(a(n)) = A317742(n).

A317742 Let b(1) = b(2) = 1; for n >= 3, b(n) = b(t(n)) + b(n-t(n)) where t = A287422. a(n) = 2*b(n) - n.

Original entry on oeis.org

1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 0, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 0, 1, 0, 1, 0, 1, 2, 3, 4, 3, 2, 1, 2, 3, 2, 3, 4, 5, 6, 5, 4, 3, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1, 0, 1, 0, 1, 0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 4, 5, 6, 5, 4, 3, 4, 5, 6, 7, 8, 9, 10
Offset: 1

Views

Author

Altug Alkan, Aug 05 2018

Keywords

Comments

This sequence has fractal-like structure as A004074, although there are substantial differences of this sequence based on slow A287422 and b(n) sequences. See plots of this sequence and A004074 in Links section.

Links

Crossrefs

Cf. A004074, A287422, A317648, A317686.

Programs

  • Maple
    t:= proc(n) option remember; `if`(n<3, 1,
      n -t(t(n-1)) -t(n-t(n-1)))
    end:
b:= proc(n) option remember; `if`(n<3, 1,
      b(t(n)) +b(n-t(n)))
    end:
seq(2*b(n)-n, n=1..100); # after Alois P. Heinz at A317686
  • Mathematica
    Block[{t = NestWhile[Function[{a, n}, Append[a, n - a[[a[[-1]] ]] - a[[-a[[-1]] ]] ] ] @@ {#, Length@ # + 1} &, {1, 1}, Last@ # < 10^2 &], b}, b = NestWhile[Function[{b, n}, Append[b, b[[t[[n]] ]] + b[[-t[[n]] ]] ] ] @@ {#, Length@ # + 1} &, {1, 1}, Last@ # < Max@ t &]; Array[2 b[[#]] - # &, Length@ b] ] (* Michael De Vlieger, Aug 07 2018 *)
t[n_] := t[n] = If[n<3, 1, n - t[t[n-1]] - t[n - t[n-1]]]; b[n_] := b[n] = If[n<3, 1, b[t[n]] + b[n - t[n]]]; Table[2*b[n] - n, {n, 106}] (* Giovanni Resta, Aug 14 2018 *)
  • PARI
    t=vector(199); t[1]=t[2]=1; for(n=3, #t, t[n] = n-t[n-t[n-1]]-t[t[n-1]]); b=vector(199); b[1]=b[2]=1; for(n=3, #b, b[n] = b[t[n]]+b[n-t[n]]); vector(199, k, 2*b[k]-k)

A249041 Number of odd terms in first n terms of A249039.

Original entry on oeis.org

1, 1, 1, 2, 3, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 7, 8, 8, 9, 10, 11, 12, 13, 13, 14, 15, 16, 16, 17, 17, 17, 18, 19, 19, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 23, 23, 23, 24, 25, 25, 26, 26, 26, 26, 27, 27, 27, 28, 29, 29, 30, 31, 32, 32, 33, 33, 33, 34, 35, 35, 36
Offset: 1

Views

Author

N. J. A. Sloane, Oct 26 2014

Keywords

Links

Crossrefs

Cf. A249039, A249040, A287422.

Programs

  • Haskell
    a249041 n = a249041_list !! (n-1)
a249041_list = tail $ scanl (\i j -> i + mod j 2) 0 a249039_list
-- Reinhard Zumkeller, Nov 11 2014
  • Maple
    See A249039.

Formula

For n > 2: a(n) = a(n-1) + A249039(n) mod 2. - Reinhard Zumkeller, Nov 11 2014
a(n) = n - a(a(n-1)) - a(n-1-a(n-1)) with a(1) = a(2) = 1. - Altug Alkan, May 01 2019

A305557 a(1) = a(2) = 1; a(n) = n - a(a(n-2)) - a(n-a(n-2)) for n > 2.

Original entry on oeis.org

1, 1, 1, 2, 2, 3, 4, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 8, 9, 9, 10, 11, 11, 12, 13, 14, 15, 16, 16, 17, 17, 18, 19, 19, 19, 20, 20, 21, 21, 21, 22, 22, 22, 22, 23, 23, 24, 24, 24, 24, 24, 24, 25, 25, 25, 26, 26, 26, 26, 27, 28, 28, 28, 28, 29, 29, 30, 31, 31, 32, 33, 33, 33, 33, 34, 35, 36, 37, 37
Offset: 1

Views

Author

Altug Alkan, Jun 21 2018

Keywords

Comments

Let a_i(n) = n - a_i(a_i(n-i)) - a_i(n-a_i(n-i)). This sequence is generated by a_2(n) with initial conditions 1, 1.

Links

Crossrefs

Cf. A005229, A287422, A305845.

Programs

  • GAP
    a:=[1,1];; for n in [3..100] do a[n]:=n-a[a[n-2]]-a[n-a[n-2]]; od; a; # Muniru A Asiru, Jun 26 2018
  • Maple
    a:=proc(n) option remember: if n<3 then 1 else n-procname(procname(n-2))-procname(n-procname(n-2)) fi; end: seq(a(n), n=1..100); # Muniru A Asiru, Jun 26 2018
  • PARI
    a=vector(99); a[1]=a[2]=1; for(n=3, #a, a[n] = n-a[a[n-2]]-a[n-a[n-2]]); a

Formula

a(n+1) - a(n) = 0 or 1 for all n >= 1 and a(n) hits every positive integer.
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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