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.

A247784 a(n) = floor(1/(e - (1 + 1/n)^n)).

Original entry on oeis.org

1, 2, 2, 3, 4, 5, 5, 6, 7, 8, 8, 9, 10, 10, 11, 12, 13, 13, 14, 15, 16, 16, 17, 18, 19, 19, 20, 21, 22, 22, 23, 24, 24, 25, 26, 27, 27, 28, 29, 30, 30, 31, 32, 33, 33, 34, 35, 35, 36, 37, 38, 38, 39, 40, 41, 41, 42, 43, 44, 44, 45, 46, 47, 47, 48, 49, 49, 50
Offset: 1

Views

Author

Clark Kimberling, Sep 24 2014

Keywords

Comments

a(n+1) - a(n) is in {0,1} for n >= 0.

Links

Crossrefs

Cf. A247778, A247785, A247786.

Programs

  • Magma
    [Floor(1/(Exp(1) - (1 + 1/n)^n)): n in [1..100]]; // G. C. Greubel, Sep 14 2018
  • Mathematica
    z = 200; t = Table[Floor[1/(E - (1 + 1/k)^k)], {k, 1, z}]   (*A247784*)
d = Differences[t]
Flatten[Position[d, 0]]  (*A247785*)
Flatten[Position[d, 1]]  (*A247786*)
  • PARI
    a(n) = floor(1/(exp(1) - (1 + 1/n)^n)); \\ Michel Marcus, Sep 26 2014

Formula

a(n) ~ 2*exp(-1) * n. - Vaclav Kotesovec, Oct 09 2014

A247786 Numbers k such that A247784(k+1) - A247784(k) = 1.

Original entry on oeis.org

1, 3, 4, 5, 7, 8, 9, 11, 12, 14, 15, 16, 18, 19, 20, 22, 23, 24, 26, 27, 28, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 45, 46, 48, 49, 50, 52, 53, 54, 56, 57, 58, 60, 61, 62, 64, 65, 67, 68, 69, 71, 72, 73, 75, 76, 77, 79, 80, 81, 83, 84, 86, 87, 88, 90
Offset: 1

Views

Author

Clark Kimberling, Sep 24 2014

Keywords

Comments

A247785 and A247786 are a complementary pair.

Links

Crossrefs

Cf. A247778, A247784, A247785.

Programs

  • Mathematica
    z = 200; t = Table[Floor[1/(E - (1 + 1/k)^k)], {k, 1, z}]  (*A247784*)
d = Differences[t]
Flatten[Position[d, 0]]  (*A247785*)
Flatten[Position[d, 1]]  (*A247786*)

A249244 Numbers k such that A249243(k+1) = A249243(k).

Original entry on oeis.org

3, 7, 11, 15, 19, 22, 26, 30, 34, 38, 41, 45, 49, 53, 56, 60, 64, 68, 72, 75, 79, 83, 87, 91, 94, 98, 102, 106, 109, 113, 117, 121, 125, 128, 132, 136, 140, 144, 147, 151, 155, 159, 162, 166, 170, 174, 178, 181, 185, 189, 193, 197, 200, 204, 208, 212, 215
Offset: 1

Views

Author

Clark Kimberling, Oct 23 2014

Keywords

Comments

A249244 and A249245 are a complementary pair, analogous to the pair A247785 and A247786.

Links

Crossrefs

Cf. A247784, A247785, A249243, A249245.

Programs

  • Mathematica
    u = Floor[Table[1/((1 + 1/n)^(n + 1) - E), {n, 1, 1000}]]; (* A249243 *)
d = Differences[u]
Flatten[Position[d, 0]]  (* A249244 *)
Flatten[Position[d, 1]]  (* A249245 *)

A249245 Numbers k such that A249243(k+1) = A249243(k) + 1.

Original entry on oeis.org

1, 2, 4, 5, 6, 8, 9, 10, 12, 13, 14, 16, 17, 18, 20, 21, 23, 24, 25, 27, 28, 29, 31, 32, 33, 35, 36, 37, 39, 40, 42, 43, 44, 46, 47, 48, 50, 51, 52, 54, 55, 57, 58, 59, 61, 62, 63, 65, 66, 67, 69, 70, 71, 73, 74, 76, 77, 78, 80, 81, 82, 84, 85, 86, 88, 89
Offset: 1

Views

Author

Clark Kimberling, Oct 23 2014

Keywords

Comments

A249244 and A249245 are a complementary pair, analogous to the pair A247785 and A247786.

Links

Crossrefs

Cf. A247784, A247785, A249243, A249244.

Programs

  • Mathematica
    u = Floor[Table[1/((1 + 1/n)^(n + 1) - E), {n, 1, 1000}]]; (* A249243 *)
d = Differences[u]
Flatten[Position[d, 0]]  (* A249244 *)
Flatten[Position[d, 1]]  (* A249245 *)
Showing 1-4 of 4 results.

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

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