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 1-3 of 3 results.

A318056 Let b(1) = b(2) = 1; for n >= 3, b(n) = n - b(t(n)) - b(n-t(n-1)) where t = A004001. a(n) = 2*b(n) - n.

Original entry on oeis.org

1, 0, -1, 0, 1, 0, 1, 0, -3, -2, -3, -2, -1, 0, -1, 0, 5, 4, 5, 4, 5, 2, 1, 2, 3, 4, 3, 0, 1, 0, 1, 0, -11, -10, -11, -10, -11, -10, -7, -6, -7, -6, -9, -10, -9, -8, -7, -8, -3, -4, -3, -2, -1, -2, -5, -4, -5, -4, -1, 0, -1, 0, -1, 0, 21, 20, 21, 20, 21, 20, 21, 16, 15, 16, 15, 16, 19, 20, 19, 20
Offset: 1

Views

Author

Altug Alkan, Aug 14 2018

Keywords

Links

Crossrefs

Cf. A004001, A317754, A317854.

Programs

  • Maple
    t:= proc(n) option remember; `if`(n<3, 1,
      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-1)))
    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] = 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-1]]; a[n_] := 2*b[n] - n; Array[a, 95] (* after Giovanni Resta at A317854 *)
  • PARI
    t=vector(99); t[1]=t[2]=1; for(n=3, #t, t[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-1]]);vector(99, k, 2*b[k]-k)

A319020 Let b_i(k) = 1 for k <= i; for n > i, b_i(n) = b_i(t(n)) + b_i(n-t(n)) where t = A063882. a(n) = 3*b_2(n)-2*n if n is even, a(n) = 3*b_4(n)-n if n is odd.

Original entry on oeis.org

2, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, 2, -1, 0, 1, -2, 0, 2, -1, 0, 1, 1, 0, 2, -1, 0, 1, -2, 0, -1, -1, 0, -2, 1, 0, -1, 2, -3, 1, 1, -3, 2, -1, 3, -2, 1, 0, -1, -1, 0, 1, -2, 0, 2, -1, 0, -2, 1, 0, -1, -1, 0, -2, 1, 0, -1, 2, 0, 1, -2, 3, -1, -1, 3, -2, 1, -3, 2, -1, 0, 1, -2, 0, 2, -4, 3, -2, 4, -3, 2, -1, 0, -2
Offset: 1

Views

Author

Altug Alkan, Sep 08 2018

Keywords

Links

Crossrefs

Cf. A063882, A317686, A317754, A317854.

Programs

  • PARI
    t=f=g=vector(200); t[1]=t[2]=t[3]=t[4]=1; for(n=5, #t, t[n] = t[n-t[n-1]]+t[n-t[n-4]]); f[1]=f[2]=1; for(n=3, #f, f[n] = f[t[n]]+f[n-t[n]]); g[1]=g[2]=g[3]=g[4]=1; for(n=5, #g, g[n] = g[t[n]]+g[n-t[n]]); vector(200, n, if(n%2==0, 3*f[n]-2*n,3*g[n]-n))

A300623 Let b(1) = 1; for n >= 2, b(n) = n - b(t(n)) - b(n-t(n-1)) where t = A302128. a(n) = 2*b(n) - n.

Original entry on oeis.org

1, -2, 1, 0, 1, -2, -1, -2, 1, 2, -1, 0, 1, 0, 1, -2, -1, 2, 3, 2, 1, -2, -1, -4, -3, 2, 3, 0, 1, -4, -3, -4, -3, -2, 1, 2, -1, 0, 5, 6, 3, 4, -5, -4, -7, -6, -3, -2, -3, 2, 3, 2, 3, 2, 1, 0, 1, -2, -1, 4, 5, 2, 3, -8, -7, -10, -9, -4, -3, -6, -5, 8, 9, 6, 7, 10, 11, 10, 5, 6, 5, 6, -1, 0, -1, 0, -1, 0, 1, -2, -1, -4, -3
Offset: 1

Views

Author

Altug Alkan, Aug 14 2018

Keywords

Comments

Sequence has a fractal-like structure. Fibonacci numbers (A000045) are determinative for the generational boundaries.

Links

Crossrefs

Cf. A302128, A318056.

Programs

  • Maple
    t:= proc(n) option remember; `if`(n<4, 1,
      t(t(n-2)) +t(n-t(n-1)))
    end:
b:= proc(n) option remember; `if`(n<2, 1,
      n -b(t(n)) -b(n-t(n-1)))
    end:
seq(2*b(n)-n, n=1..100); # after Alois P. Heinz at A317686
  • Mathematica
    t[1]=t[2]=t[3]=1; t[n_] := t[n] = t[t[n-2]] + t[n - t[n-1]]; b[1]=1; b[n_] := b[n] = n - b[t[n]] - b[n - t[n-1]]; a[n_] := 2*b[n] - n; Array[a, 95] (* after Giovanni Resta at A317854 *)
  • PARI
    t=vector(99); t[1]=t[2]=t[3]=1; for(n=4, #t, t[n] = t[n-t[n-1]]+t[t[n-2]]); b=vector(99); b[1]=1; for(n=2, #b, b[n] = n-b[t[n]]-b[n-t[n-1]]); vector(99,k, 2*b[k]-k)
Showing 1-3 of 3 results.

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