A083812 -id:A083812 - cp's OEIS frontend

A086573 a(n) = 2*(10^n - 1).

0, 18, 198, 1998, 19998, 199998, 1999998, 19999998, 199999998, 1999999998, 19999999998, 199999999998, 1999999999998, 19999999999998, 199999999999998, 1999999999999998, 19999999999999998, 199999999999999998, 1999999999999999998, 19999999999999999998, 199999999999999999998

Offset: 0

Ray Chandler, Jul 22 2003

Original definition: a(n) = k where R(k+2) = 2.

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

Cf. A002275, A004086 (R(n)), A083812.

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.

a(n) = 2*9*A002275(n) = 2*A002283(n).
R(a(n)) = A086580(n).
From Chai Wah Wu, Jul 08 2016: (Start)
a(n) = 11*a(n-1) - 10*a(n-2) for n > 1.
G.f.: 18*x/((1 - x)*(1 - 10*x)). (End)
E.g.f.: 2*exp(x)*(exp(9*x) - 1). - Elmo R. Oliveira, Sep 12 2024

Edited by Jinyuan Wang, Aug 04 2021

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

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

nonn

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

Essentially a duplicate of A086574.

Cf. A000042, A083811, A083812.

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

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

A086573 a(n) = 2*(10^n - 1).

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

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

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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.

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