A010734 -id:A010734 - cp's OEIS frontend

A044712 Numbers n such that string 8,8 occurs in the base 9 representation of n but not of n+1.

80, 161, 242, 323, 404, 485, 566, 647, 728, 809, 890, 971, 1052, 1133, 1214, 1295, 1376, 1457, 1538, 1619, 1700, 1781, 1862, 1943, 2024, 2105, 2186, 2267, 2348, 2429, 2510, 2591, 2672, 2753, 2834, 2915, 2996, 3077, 3158

Offset: 1

Clark Kimberling

Tanya Khovanova, Non Recursions

Cf. A157597, A010734 [From Vincenzo Librandi, Mar 13 2009]

SequencePosition[Table[If[SequenceCount[IntegerDigits[n,9],{8,8}]>0,1,0],{n,3200}],{1,0}][[All,1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 23 2017 *)

A140684 A037481 mod 10.

Original entry on oeis.org

0, 1, 6, 5, 2, 9, 8, 3, 4, 7, 0, 1, 6, 5, 2, 9, 8, 3, 4, 7, 0, 1, 6, 5, 2, 9, 8, 3, 4, 7, 0, 1, 6, 5, 2, 9, 8, 3, 4, 7, 0, 1, 6, 5, 2, 9, 8, 3, 4, 7, 0, 1, 6, 5, 2, 9, 8, 3, 4, 7, 0, 1, 6, 5, 2, 9, 8, 3, 4, 7, 0, 1, 6, 5, 2, 9, 8, 3, 4, 7, 0, 1, 6, 5, 2, 9, 8, 3, 4, 7, 0, 1, 6, 5, 2, 9, 8, 3, 4, 7, 0, 1, 6, 5, 2

Offset: 0

Paul Curtz, Jul 11 2008

The sequence is periodic with length 10 and contains all 10 digits.

The first differences 1, 5, -1, -3, 7, -1, -5, 1, 3, -7 are also periodic with period length 10.

a(n) = A037481(n) mod 10. a(n)= a(n-10).
a(n)+a(n+5)= A010734(n).
O.g.f.: (7x^4-3x^3-x^2+5x+1)x/((1-x)(1+x)(x^4-x^3+x^2-x+1)). - R. J. Mathar, Jul 14 2008

Edited by R. J. Mathar, Jul 14 2008

A291092 1 followed by infinitely many 9's.

Original entry on oeis.org

1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9

Offset: 1

N. J. A. Sloane, Aug 19 2017

The digital root of 9^(n-1). - Cino Hilliard, Dec 31 2004

With interpolated zeros (1,0,9,0,9,0,9,0,...) this is the number of hours between times when the hands of a two-handed clock cross. - Halfdan Skjerning, Aug 18 2017

Brady Haran and Cliff Stoll, When do clock hands overlap?, Numberphile video (2017)
Index entries for linear recurrences with constant coefficients, signature (1).

Cf. A178181, A010734, A180599, A100403, A100401.

PadRight[{1},100,9] (* Paolo Xausa, Oct 16 2023 *)

G.f.: x*(1 + 8*x)/(1 - x). - Chai Wah Wu, Aug 19 2017

E.g.f.: 9*(exp(x) - 1) - 8*x. - Stefano Spezia, Oct 16 2023

cp's OEIS Frontend

A044712 Numbers n such that string 8,8 occurs in the base 9 representation of n but not of n+1.

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A140684 A037481 mod 10.

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A291092 1 followed by infinitely many 9's.

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