A083813 -id:A083813 - cp's OEIS frontend

A086574 a(n) = 3*(10^n - 1).

0, 27, 297, 2997, 29997, 299997, 2999997, 29999997, 299999997, 2999999997, 29999999997, 299999999997, 2999999999997, 29999999999997, 299999999999997, 2999999999999997, 29999999999999997, 299999999999999997, 2999999999999999997, 29999999999999999997, 299999999999999999997

Offset: 0

Ray Chandler, Jul 22 2003

Original definition: a(n) = k where R(k+3) = 3. [Here R = reverse = A004086, not R = repunit = A002275 as in some other places.]

The restriction to positive indices yields A083813. - M. F. Hasler, Jul 29 2016

Index entries for linear recurrences with constant coefficients, signature (11,-10).

Cf. A002275, A004086 (R(n)), A083813.

Cf. 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.

Join[{0},Table[FromDigits[Join[PadRight[{2},n,9],{7}]],{n,20}]] (* or *) LinearRecurrence[{11,-10},{0,27},30] (* Harvey P. Dale, Nov 28 2015 *)

a(n)=10^n*3-3 \\ M. F. Hasler, Jul 29 2016

a(n) = 3*9*A002275(n) = 3*A002283(n).
R(a(n)) = A086579(n).
a(n) = 11*a(n-1) - 10*a(n-2) with a(0)=0 and a(1)=27. - Harvey P. Dale, Nov 28 2015
G.f.: 27*x/((1 - x)*(1 - 10*x)). - Ilya Gutkovskiy, Jul 29 2016
E.g.f.: 3*exp(x)*(exp(9*x) - 1). - Elmo R. Oliveira, Sep 12 2024

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

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

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).

			2*37 - 1 = 73.

Index entries for linear recurrences with constant coefficients, signature (11,-10).

Cf. A000042, A083811, A083812, A083813.

Digit reversals of A169830.

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

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)

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

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

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

Cf. A083811, A083812, A083813, A083818.

Corrected and extended by Ray Chandler, Jun 23 2003

cp's OEIS Frontend

A086574 a(n) = 3*(10^n - 1).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Formula

Extensions

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.

Views

Author

Keywords

Examples

Crossrefs

Extensions