A098210 -id:A098210 - cp's OEIS frontend

A099638 a[n]=A098210[n]/15.

1, 77, 7437, 741037, 74077037, 7407437037, 740741037037, 74074077037037, 7407407437037037, 740740741037037037, 74074074077037037037, 7407407407437037037037, 740740740741037037037037

Offset: 1

Labos Elemer, Oct 28 2004

nonn

Patterned-digit obtained when (1,5)-half-repdigit is divided by 15, the least such number.This simple generating rule is often[not always] applicable to provide curious digit-patterns. Thus A=1,B=7 give 111..888 numbers divided by 18 results in A003555.

			n = 20: a[20] = 1111111111111111111155555555555555555555/15 = 74074074074074074077037037037037037037.

Cf. A098210.

f[x_] := 3*((100^x-1)/9) + 4*(10^x-1)/9 Table[f[w], {w, 1, 20}]/15

a[n]=A*(((100^n-1)/9)+B*(10^n - 1)/9)/15, where A=1, B=5-A=4.

A003555 Sum_{i=1..(10^n - 1)/9} i, or ((10^n -1)/9)*((10^n -1)/9 +1)/2 (n-th term is the middle 2(n-1) digits of the (n+9)-th term for n > 1).

Original entry on oeis.org

1, 66, 6216, 617716, 61732716, 6172882716, 617284382716, 61728399382716, 6172839549382716, 617283951049382716, 61728395066049382716, 6172839506216049382716, 617283950617716049382716, 61728395061732716049382716, 6172839506172882716049382716

Offset: 1

Daniel Lawson (dlawson(AT)cats.ucsc.edu)

Patterned, or almost palindromic, numbers obtained by modification of "half-repdigit" numbers. a[n]=A*(((100^n-1)/9)+B*(10^n - 1)/9)/18, where A=1, B=8-A=7. For example, n = 20: a[20] = 1111111111111111111188888888888888888888/18 = 61728395061728395066049382716049382716, an "almost-palindromic-number". - Labos Elemer, Oct 28 2004

n is "almost palindromic" if digitlist-Rev[digitlist], besides zeros, contains +1 or -1 in "regular" positions. - Labos Elemer, Oct 28 2004

Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

Cf. A002275, A093142, A098210, A099638.

f[x_] := 1*((100^x-1)/9) + 7*(10^x-1)/9 Table[f[w], {w, 1, 20}]/18 (* Labos Elemer, Oct 28 2004 *)

Vec(x*(-1+45*x)/((x-1)*(100*x-1)*(10*x-1))+O(x^99)) \\ Charles R Greathouse IV, Jun 23 2020

a(n) = A002275(n) * A093142(n).

G.f.: x*(-1+45*x) / ( (x-1)*(100*x-1)*(10*x-1) ). - R. J. Mathar, Mar 10 2011

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 31 2007

A184337 a(n) is the integer whose decimal representation consists of n 8's followed by n 1's.

Original entry on oeis.org

0, 81, 8811, 888111, 88881111, 8888811111, 888888111111, 88888881111111, 8888888811111111, 888888888111111111, 88888888881111111111, 8888888888811111111111, 888888888888111111111111, 88888888888881111111111111

Offset: 0

Paul Curtz, Feb 13 2011

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Richard Blecksmith and Charles Nicol, Monotonic Numbers, Mathematics Magazine, 66, (1993), 257-262.
Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

Cf. A098210 (with 1 and 5 instead of 8 and 1).
Cf. A002283, A059482.
Cf. A008591 (digits sums).

[(8*100^n-7*10^n-1)/9: n in [0..20]]; // Vincenzo Librandi, Aug 04 2011

Table[(8*100^n - 7*10^n - 1)/9, {n,0,30}] (* G. C. Greubel, Nov 02 2018 *)
FromDigits/@Table[Join[PadRight[{},n,8],PadRight[{},n,1]],{n,0,15}] (* or *) LinearRecurrence[ {111,-1110,1000},{0,81,8811},15] (* Harvey P. Dale, Jul 03 2023 *)

vector(30, n, n--; (8*100^n - 7*10^n - 1)/9) \\ G. C. Greubel, Nov 02 2018

for n in range(30):
    print((8*100**n-7*10**n-1)//9, end=', ')
# Stefano Spezia, Nov 02 2018

a(n) = (8*100^n - 7*10^n - 1)/9.
a(n) = A059482(n)*A002283(n).
G.f.: 9*x*(-9+20*x) / ( (x-1)*(100*x-1)*(10*x-1) ). - R. J. Mathar, Feb 28 2011

cp's OEIS Frontend

A099638 a[n]=A098210[n]/15.

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A003555 Sum_{i=1..(10^n - 1)/9} i, or ((10^n -1)/9)*((10^n -1)/9 +1)/2 (n-th term is the middle 2(n-1) digits of the (n+9)-th term for n > 1).

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A184337 a(n) is the integer whose decimal representation consists of n 8's followed by n 1's.

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