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 1-5 of 5 results.

A086575 a(n) = 4*(10^n - 1).

Original entry on oeis.org

0, 36, 396, 3996, 39996, 399996, 3999996, 39999996, 399999996, 3999999996, 39999999996, 399999999996, 3999999999996, 39999999999996, 399999999999996, 3999999999999996, 39999999999999996, 399999999999999996, 3999999999999999996, 39999999999999999996, 399999999999999999996
Offset: 0

Views

Author

Ray Chandler, Jul 22 2003

Keywords

Comments

Original definition: a(n) = k where R(k+4) = 4.

Links

Crossrefs

Cf. A002275, A004086 (R(n)), A083811.
One of family of sequences of form a(n) = k, where R(k+m) = m, m=1 to 9; m=1: A002283, m=2: A086573, m=3: A086574, m=4: A086575, m=5: A086576, m=6: A086577, m=7: A086578, m=8: A086579, m=9: A086580.

Programs

  • Mathematica
    LinearRecurrence[{11,-10},{0,36},20] (* Harvey P. Dale, May 14 2017 *)

Formula

a(n) = 4*9*A002275(n) = 4*A002283(n).
R(a(n)) = A086578(n).
From Chai Wah Wu, Jul 08 2016: (Start)
a(n) = 11*a(n-1) - 10*a(n-2) for n > 1.
G.f.: 36*x/((1 - x)*(1 - 10*x)). (End)
E.g.f.: 4*exp(x)*(exp(9*x) - 1). - Elmo R. Oliveira, Sep 12 2024

Extensions

Edited by Jinyuan Wang, Aug 04 2021

A083812 4n-1 is the digit reversal of n-1.

Original entry on oeis.org

18, 198, 1998, 19998, 199998, 1999998, 19999998, 199999998, 1999999998, 19999999998, 199999999998, 1999999999998, 19999999999998, 199999999999998, 1999999999999998, 19999999999999998, 199999999999999998, 1999999999999999998, 19999999999999999998
Offset: 1

Views

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 08 2003

Keywords

Comments

1. a(n) = 18 + 180 + 1800+ ...+ up to n terms. a(n) = sum of n terms of the geometric progression with the first term 18 and common ratio 10. 2. a(n) = 18*A000042(n).( the unary sequence).

Examples

			18 -1 = 17, 4*18 - 1 = 71.

Links

Crossrefs

Cf. A000042, A083811.

Programs

  • Mathematica
    Accumulate[NestList[10#&,18,20]] (* or *) LinearRecurrence[{11,-10},{18,198},20] (* Harvey P. Dale, Apr 24 2015 *)

Formula

a(n) = 2*(10^n - 1).
a(1)=18, a(2)=198, a(n)=11*a(n-1)-10*a(n-2). - Harvey P. Dale, Apr 24 2015

Extensions

Corrected and extended by Harvey P. Dale, Apr 24 2015

A083813 a(n) = 3*(10^n-1).

Original entry on oeis.org

27, 297, 2997, 29997, 299997, 2999997, 29999997, 299999997, 2999999997, 29999999997, 299999999997, 2999999999997, 29999999999997, 299999999999997
Offset: 1

Views

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 08 2003

Keywords

Comments

Original definition: 3n+1 is the digit reversal of n+1.
1. a(n) = 27 + 270 + 2700 + ... up to n terms = sum of n terms of the geometric progression with the first term 27 and common ratio 10.
2. a(n) = 27*A000042(n) (the unary sequence).
Equals A086574 restricted to positive indices. See that entry for many more comments, formulas and references. - M. F. Hasler, Jul 29 2016

Crossrefs

Essentially a duplicate of A086574.
Cf. A000042, A083811, A083812.

Programs

  • Mathematica
    3(10^Range[20]-1) (* or *) Table[10 FromDigits[PadRight[{2},n,9]]+7,{n,20}] (* Harvey P. Dale, Jan 25 2020 *)

Extensions

Edited by M. F. Hasler, Jul 29 2016

A083818 Numbers k such that 2k-1 is the digit reversal of k.

Original entry on oeis.org

1, 37, 397, 3997, 39997, 399997, 3999997, 39999997, 399999997, 3999999997, 39999999997, 399999999997, 3999999999997, 39999999999997, 399999999999997, 3999999999999997, 39999999999999997, 399999999999999997, 3999999999999999997, 39999999999999999997, 399999999999999999997
Offset: 1

Views

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 08 2003

Keywords

Comments

a(n) = 1 + 36 + 360 + 3600 + 36000 + ..., for a total of n terms. a(n) = 1 + sum of first n-1 terms of the geometric progression with first term 36 and common ratio 10. a(n) = 1 + 36*A000042(n-1) (the unary sequence).

Examples

			2*37 - 1 = 73.

Links

Crossrefs

Cf. A000042, A083811, A083812, A083813.
Digit reversals of A169830.

Programs

  • PARI
    my(x='x+O('x^22)); Vec(x*(1+26*x)/((1-x)*(1-10*x))) \\ Elmo R. Oliveira, Jun 12 2025

Formula

a(n) = 4*10^(n-1) - 3.
From Elmo R. Oliveira, Jun 12 2025: (Start)
G.f.: x*(26*x+1)/((x-1)*(10*x-1)).
E.g.f.: (13 - 15*exp(x) + 2*exp(10*x))/5.
a(n) = 11*a(n-1) - 10*a(n-2) for n >= 3. (End)

Extensions

a(1)=1 inserted by David Radcliffe, Jul 25 2015

A083819 a(1) = 1, then the smallest k > 1 such that nk + 1 is the digit reversal of k + 1, or 0 if no such number exists.

Original entry on oeis.org

1, 36, 27, 15, 18, 11385, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
Offset: 1

Views

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 08 2003

Keywords

Examples

			a(2) = 36: 2*36 + 1 = 73, 37 = 36 + 1.
a(5) = 18: 18*5 + 1 = 91, 19 = 18 + 1.

Crossrefs

Cf. A083811, A083812, A083813, A083818.

Extensions

Corrected and extended by Ray Chandler, Jun 23 2003
Showing 1-5 of 5 results.

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