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.

A099674 Partial sums of repdigits of A002281.

Original entry on oeis.org

0, 7, 84, 861, 8638, 86415, 864192, 8641969, 86419746, 864197523, 8641975300, 86419753077, 864197530854, 8641975308631, 86419753086408, 864197530864185, 8641975308641962, 86419753086419739, 864197530864197516, 8641975308641975293, 86419753086419753070, 864197530864197530847
Offset: 0

Views

Author

Labos Elemer, Nov 17 2004

Keywords

Examples

			7 + 77 + 777 + 7777 + 77777 = a(5) = 86415.

Links

Crossrefs

Cf. A002275-A002283, A014824, A057932, A099669-A099675.

Programs

  • Mathematica
    <Robert G. Wilson v, Nov 20 2004 *)
Accumulate[LinearRecurrence[{11,-10},{0,7},25]] (* Harvey P. Dale, Jul 22 2025 *)

Formula

a(n) = (7/81)*(10^(n+1) - 9*n - 10). - R. Piyo (nagoya314(AT)yahoo.com), Dec 10 2004
From Elmo R. Oliveira, Apr 02 2025: (Start)
G.f.: 7*x/((1 - x)^2*(1 - 10*x)).
E.g.f.: 7*exp(x)*(10*exp(9*x) - 9*x - 10)/81.
a(n) = 7*A014824(n).
a(n) = 12*a(n-1) - 21*a(n-2) + 10*a(n-3) for n > 3. (End)

Extensions

More terms from Elmo R. Oliveira, Apr 02 2025
a(0)=0 prepended by Harvey P. Dale, Jul 22 2025

A099672 Partial sums of repdigits of A002279.

Original entry on oeis.org

5, 60, 615, 6170, 61725, 617280, 6172835, 61728390, 617283945, 6172839500, 61728395055, 617283950610, 6172839506165, 61728395061720, 617283950617275, 6172839506172830, 61728395061728385, 617283950617283940, 6172839506172839495, 61728395061728395050, 617283950617283950605
Offset: 1

Views

Author

Labos Elemer, Nov 17 2004

Keywords

Examples

			5 + 55 + 555 + 5555 + 55555 = a(5) = 61725.

Links

Crossrefs

Cf. A002275-A002283, A014824, A057932, A099669-A099675.

Programs

  • Mathematica
    <Robert G. Wilson v, Nov 20 2004 *)
Accumulate[Table[FromDigits[PadRight[{},n,5]],{n,0,20}]] (* Harvey P. Dale, Oct 05 2013 *)
  • PARI
    Vec(5*x/((1 - x)^2*(1 - 10*x)) + O(x^40)) \\ Colin Barker, Nov 30 2017

Formula

a(n) = (5/81)*(10^(n+1) - 9*n - 10). - R. Piyo (nagoya314(AT)yahoo.com), Dec 10 2004.
From Colin Barker, Nov 30 2017: (Start)
G.f.: 5*x/((1 - x)^2*(1 - 10*x)).
a(n) = 12*a(n-1) - 21*a(n-2) + 10*a(n-3) for n > 3. (End)
From Elmo R. Oliveira, Apr 03 2025: (Start)
E.g.f.: 5*exp(x)*(10*exp(9*x) - 9*x - 10)/81.
a(n) = 5*A014824(n). (End)

A099673 Partial sums of repdigits of A002280.

Original entry on oeis.org

6, 72, 738, 7404, 74070, 740736, 7407402, 74074068, 740740734, 7407407400, 74074074066, 740740740732, 7407407407398, 74074074074064, 740740740740730, 7407407407407396, 74074074074074062, 740740740740740728, 7407407407407407394, 74074074074074074060, 740740740740740740726
Offset: 1

Views

Author

Labos Elemer, Nov 17 2004

Keywords

Examples

			6 + 66 + 666 + 6666 + 66666 = a(5) = 74070.

Links

Crossrefs

Cf. A002275-A002283, A014824, A057932, A099669-A099675.

Programs

  • Mathematica
    <Robert G. Wilson v, Nov 20 2004 *)

Formula

a(n) = (2/27)*(10^(n+1) - 9*n - 10). - R. Piyo (nagoya314(AT)yahoo.com), Dec 10 2004
From Elmo R. Oliveira, Apr 02 2025: (Start)
G.f.: 6*x/((1 - x)^2*(1 - 10*x)).
a(n) = 6*A014824(n).
E.g.f.: 2*exp(x)*(10*exp(9*x) - 9*x - 10)/27.
a(n) = 12*a(n-1) - 21*a(n-2) + 10*a(n-3) for n > 3. (End)

Extensions

More terms from Elmo R. Oliveira, Apr 02 2025
Showing 1-3 of 3 results.

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