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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.

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A015585 a(n) = 9*a(n-1) + 10*a(n-2).

Original entry on oeis.org

0, 1, 9, 91, 909, 9091, 90909, 909091, 9090909, 90909091, 909090909, 9090909091, 90909090909, 909090909091, 9090909090909, 90909090909091, 909090909090909, 9090909090909091, 90909090909090909, 909090909090909091, 9090909090909090909, 90909090909090909091
Offset: 0

Views

Author

Olivier Gérard

Keywords

Comments

Number of walks of length n between any two distinct nodes of the complete graph K_11. Example: a(2)=9 because the walks of length 2 between the nodes A and B of the complete graph ABCDEFGHIJK are: ACB, ADB, AEB, AFB, AGB, AHB, AIB, AJB and AKB. - Emeric Deutsch, Apr 01 2004
Beginning with n=1 and a(1)=1, these are the positive integers whose balanced base-10 representations (A097150) are the first n digits of 1,-1,1,-1,.... Also, a(n) = (-1)^(n-1)*A014992(n) = |A014992(n)| for n >= 1. - Rick L. Shepherd, Jul 30 2004
General form: k=10^n-k. Also: A001045, A078008, A097073, A115341, A015518, A054878, A015521, A109499, A015531, A109500, A109501, A015552, A093134, A015565, A015577. - Vladimir Joseph Stephan Orlovsky, Dec 11 2008

Links

Crossrefs

Cf. A014992 (q-integers for q=-10), A097150.
Cf. A001045, A078008, A097073, A115341, A015518, A054878, A015521, A109499, A015531, A109500, A109501, A015552, A093134, A015565, A015577. - Vladimir Joseph Stephan Orlovsky, Dec 11 2008
Cf. A094028, A098610, A098611.

Programs

Formula

a(n) = 9*a(n-1) + 10*a(n-2).
From Emeric Deutsch, Apr 01 2004: (Start)
a(n) = 10^(n-1) - a(n-1).
G.f.: x/(1 - 9x - 10x^2). (End)
From Henry Bottomley, Sep 17 2004: (Start)
a(n) = round(10^n/11).
a(n) = (10^n - (-1)^n)/11.
a(n) = A098611(n)/11 = 9*A094028(n+1)/A098610(n). (End)
E.g.f.: exp(-x)*(exp(11*x) - 1)/11. - Elmo R. Oliveira, Aug 17 2024

Extensions

Extended by T. D. Noe, May 23 2011

A097151 Digits of balanced base-10 representations of nonnegative integers (least significant digits first).

Original entry on oeis.org

0, 1, 2, 3, 4, -5, 1, -4, 1, -3, 1, -2, 1, -1, 1, 0, 1, 1, 1, 2, 1, 3, 1, 4, 1, -5, 2, -4, 2, -3, 2, -2, 2, -1, 2, 0, 2, 1, 2, 2, 2, 3, 2, 4, 2, -5, 3, -4, 3, -3, 3, -2, 3, -1, 3, 0, 3, 1, 3, 2, 3, 3, 3, 4, 3, -5, 4, -4, 4, -3, 4, -2, 4, -1, 4, 0, 4, 1, 4, 2, 4, 3, 4, 4, 4, -5, -5, 1, -4, -5, 1, -3, -5, 1, -2, -5, 1, -1, -5, 1, 0, -5, 1, 1, -5, 1, 2, -5, 1, 3, -5, 1
Offset: 1

Views

Author

Rick L. Shepherd, Jul 27 2004

Keywords

Comments

Definition 9.1.2. of the Crandall-Pomerance book is: "The balanced base-B representation of a nonnegative integer x is the shortest sequence of integer digits (x_i) such that each digit satisfies -floor(B/2) <= x_i <= floor((B-1)/2) and x = sum(i=0,D-1,x_i*B^i)." (I have replaced floor and sigma symbols with "floor" and "sum" for inclusion here.) The D digits x_0, x_1, x_2, ..., x_(D-1) are included in this order in this sequence and in the opposite order in A097150.

Examples

			As the only digits permissible are in {-5,-4,-3,-2,-1,0,1,2,3,4},
5 = -5 + 1*10 is the first number requiring two of these digits: -5,1.
A097150 is the same sequence but with the digits in reverse order.
Also, 45 = -5 - 5*10 + 1*10^2 has digits -5,-5,1,
54 = 4 - 5*10 + 1*10^2 has digits 4,-5,1 and
55 = -5 - 4*10 + 1*10^2 has digits -5,-4,1.

References

  • R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see p. 408.

Crossrefs

Cf. A097150 (most significant digits first).
Showing 1-2 of 2 results.

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