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 1-10 of 20 results. Next

A298520 Decimal expansion of lim_ {n->oo} (s(0) + s(1) + ... + s(n) - (n+1)*g), where g = 1.324717957..., s(n) = (s(n - 1) + 1)^(1/3), s(0) = 3.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Feb 11 2018

Keywords

Comments

(lim_ {n->oo} s(n)) = g = real zero of x^3 - x - 1. See A298512 for a guide to related sequences.

Examples

			s(0) + s(1) + ... + s(n) - (n+1)*g -> 1.9972964760109796754339092295853245...

Crossrefs

Cf. A298512, A298518, A298519.

Programs

  • Mathematica
    s[0] = 3; d = 1; p = 1/3;
g = (x /. NSolve[x^(1/p) - x - d == 0, x, 200])[[3]]
s[n_] := s[n] = (s[n - 1] + d)^p
N[Table[s[n], {n, 0, 30}]]
s = N[Sum[- g + s[n], {n, 0, 200}], 150 ];
RealDigits[s, 10][[1]] (* A298520 *)

A298522 Decimal expansion of lim_ {n->oo} ((n + 1)*g - s(0) - s(1) - ... - s(n)), where g = 1.86676039917386..., s(n) = (s(n - 1) + (1+sqrt(5))/2)^(1/2), s(0) = 1.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Feb 12 2018

Keywords

Comments

(lim_ {n->oo} s(n)) = g = real zero of x^2 - x - (1+sqrt(5))/2. See A298512 for a guide to related sequences.

Examples

			((n + 1)*g - s(0) - s(1) - ... - s(n)) -> 1.20829379722676782518591549956095278...

Crossrefs

Cf. A298512, A298523.

Programs

  • Mathematica
    s[0] = 1; d = GoldenRatio; p = 1/2;
g = (x /. NSolve[x^(1/p) - x - d == 0, x, 200])[[2]]
s[n_] := s[n] = (s[n - 1] + d)^p
N[Table[s[n], {n, 0, 30}]]
s = N[Sum[g - s[n], {n, 0, 200}], 150 ];
RealDigits[s, 10][[1]] (* A298522 *)

A298516 Decimal expansion of lim_ {n->oo} (2n+2 - s(0) - s(1) - ... - s(n)), where s(n) = (s(n - 1) + 2)^(1/2), s(0) = 1.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Feb 11 2018

Keywords

Comments

See A298512 for a guide to related sequences.

Examples

			2n + 2 - s(0) - s(1) - ... - s(n) -> 1.358917762842788340395837672187105945234...

Crossrefs

Cf. A298512, A298516, A298517.

Programs

  • Mathematica
    s[0] = 1; d = 2; p = 1/2;
g = (x /. NSolve[x^(1/p) - x - d == 0, x, 200])[[2]]
s[n_] := s[n] = (s[n - 1] + d)^p
N[Table[s[n], {n, 0, 30}]];
s = N[Sum[g - s[n], {n, 0, 200}], 150 ];
StringJoin[StringTake[ToString[s], 41], "..."]
u = RealDigits[s, 10][[1]]   (* A298516 *)

A298517 Decimal expansion of lim_ {n->oo} ((n + 1)*g - s(0) - s(1) - ... - s(n)), where g = (1 + sqrt (13))/2, s(n) = (s(n - 1) + 3)^(1/2), s(0) = 1.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Feb 11 2018

Keywords

Comments

(lim_ {n->oo} s(n)) = g = (1 + sqrt (13))/2. See A298512 for a guide to related sequences.

Examples

			((n + 1)*g - s(0) - s(1) - ... - s(n)) -> 0.91504984801513491484363121460300...

Crossrefs

Cf. A298512, A298515, A298516.

Programs

  • Mathematica
    s[0] = 1; d = 3; p = 1/2; s[n_] := s[n] = (s[n - 1] + d)^p
N[Table[s[n], {n, 0, 30}]]
z = 200 ; g = (1 + Sqrt[13])/2;
s = N[(z + 1)*g - Sum[s[n], {n, 0, z}], 150 ];
RealDigits[s, 10][[1]];  (* A298517 *)

A298518 Decimal expansion of lim_ {n->oo} ((n + 1)*g - s(0) - s(1) - ... - s(n)), where g = 1.324717957..., s(n) = (s(n - 1) + 1)^(1/3), s(0) = 1.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Feb 11 2018

Keywords

Comments

(lim_ {n->oo} s(n)) = g = real zero of x^3 - x - 1. See A298512 for a guide to related sequences.

Examples

			((n + 1)*g - s(0) - s(1) - ... - s(n)) -> 0.40485767742624961326290607445802...

Crossrefs

Cf. A298512, A298519, A298520.

Programs

  • Mathematica
    s[0] = 1; d = 1; p = 1/3;
g = (x /. NSolve[x^(1/p) - x - d == 0, x, 200])[[3]]
s[n_] := s[n] = (s[n - 1] + d)^p
N[Table[s[n], {n, 0, 30}]]
s = N[Sum[g - s[n], {n, 0, 200}], 150 ];
RealDigits[s, 10][[1]] (* A298518 *)

A298519 Decimal expansion of lim_ {n->oo} (s(0) + s(1) + ... + s(n) - (n+1)*g), where g = 1.324717957..., s(n) = (s(n - 1) + 1)^(1/3), s(0) = 2.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Feb 11 2018

Keywords

Comments

(lim_ {n->oo} s(n)) = g = real zero of x^3 - x - 1. See A298512 for a guide to related sequences.

Examples

			s(0) + s(1) + ... + s(n) - (n+1)*g -> 0.819904707664104372564776035917499198052...

Crossrefs

Cf. A298512, A298518, A298520.

Programs

  • Mathematica
    s[0] = 2; d = 1; p = 1/3;
g = (x /. NSolve[x^(1/p) - x - d == 0, x, 200])[[3]]
s[n_] := s[n] = (s[n - 1] + d)^p
N[Table[s[n], {n, 0, 30}]]
s = N[Sum[-g + s[n], {n, 0, 200}], 150 ];
RealDigits[s, 10][[1]] (* A298519 *)

A298523 Decimal expansion of lim_ {n->oo} (s(0) + s(1) + ... + s(n) - (n + 1)*g), where g = 1.86676039917386..., s(n) = (s(n - 1) + (1+sqrt(5))/2)^(1/2), s(0) = 2.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Feb 12 2018

Keywords

Comments

(lim_ {n->oo} s(n)) = g = real zero of x^2 - x - (1+sqrt(5))/2. See A298512 for a guide to related sequences.

Examples

			s(0) + s(1) + ... + s(n) - (n + 1)*g -> 0.1814900833342507808225393126374219...

Crossrefs

Cf. A298512, A298522.

Programs

  • Mathematica
    s[0] = 2; d = GoldenRatio; p = 1/2;
g = (x /. NSolve[x^(1/p) - x - d == 0, x, 200])[[2]]
s[n_] := s[n] = (s[n - 1] + d)^p
N[Table[s[n], {n, 0, 30}]]
s = N[Sum[- g + s[n], {n, 0, 200}], 150 ];
RealDigits[s, 10][[1]] (* A298523 *)

A298526 Decimal expansion of lim_ {n->oo} ((n+1)*g - s(0) - s(1) - ... - s(n)), where g = 1.9078532620869538..., s(n) = (s(n - 1) + sqrt(3))^(1/2), s(0) = 1.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Feb 12 2018

Keywords

Comments

(lim_ {n->oo} s(n)) = g = positive zero of x^2 - x - sqrt(3). See A298512 for a guide to related sequences.

Examples

			(n+1)*g - s(0) - s(1) - ... - s(n) -> 1.255130808144253924335186404635816957676...

Crossrefs

Cf. A298512, A298527.

Programs

  • Mathematica
    s[0] = 1; d = Sqrt[3]; p = 1/2;
g = (x /. NSolve[x^(1/p) - x - d == 0, x, 200])[[2]]
s[n_] := s[n] = (s[n - 1] + d)^p
N[Table[s[n], {n, 0, 30}]]
s = N[Sum[g - s[n], {n, 0, 200}], 150 ];
RealDigits[s, 10][[1]] (* A298526 *)

A298531 Decimal expansion of lim_ {n->oo} (s(0) + s(1) + ... + s(n) - (n+1)*g), where g = 2.3416277185114784317..., s(n) = (s(n - 1) + Pi)^(1/2), s(0) = Pi.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Feb 12 2018

Keywords

Comments

(lim_ {n->oo} s(n)) = g = positive zero of x^2 - x - Pi. See A298512 for a guide to related sequences.

Examples

			lim_ {n->oo} (s(0) + s(1) + ... + s(n) - (n+1)*g) -> 1.009415125594648468509...

Crossrefs

Cf. A298512, A298530.

Programs

  • Mathematica
    s[0] = Pi; d = Pi; p = 1/2;
g = (x /. NSolve[x^(1/p) - x - d == 0, x, 200])[[2]]
s[n_] := s[n] = (s[n - 1] + d)^p
N[Table[s[n], {n, 0, 30}]]
s = N[Sum[-g + s[n], {n, 0, 200}], 150 ];
RealDigits[s, 10][[1]] (* A298531 *)

A298513 Decimal expansion of lim_ {n->oo} (s(0) + s(1) + ... + s(n) - (n + 1)*g), where g = (1 + sqrt (5))/2, s(n) = (s(n - 1) + 1)^(1/2), s(0) = 2.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Feb 11 2018

Keywords

Comments

(lim_ {n->oo} s(n)) = g = golden ratio, A001622. See A298512 for a guide to related sequences.

Examples

			s(n) -> g = (1+sqrt(5))/2, as at A001622.
s(0) + s(1) + ... + s(n) - (n + 1)*g -> 0.54637233477988845286584405518616478...

Crossrefs

Cf. A001622, A298512, A298514.

Programs

  • Mathematica
    s[0] = 2; d = 1; p = 1/2; s[n_] := s[n] = (s[n - 1] + d)^p
N[Table[s[n], {n, 0, 30}]]
z = 200 ; g = GoldenRatio; s = N[-(z + 1)*g + Sum[s[n], {n, 0, z}], 150 ];
RealDigits[s, 10][[1]];  (* A298513 *)
Showing 1-10 of 20 results. Next

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