cp's OEIS Frontend

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.

A047393 Numbers that are congruent to {0, 1} mod 8.

Original entry on oeis.org

0, 1, 8, 9, 16, 17, 24, 25, 32, 33, 40, 41, 48, 49, 56, 57, 64, 65, 72, 73, 80, 81, 88, 89, 96, 97, 104, 105, 112, 113, 120, 121, 128, 129, 136, 137, 144, 145, 152, 153, 160, 161, 168, 169, 176, 177, 184, 185, 192, 193, 200, 201, 208, 209, 216, 217, 224, 225, 232
Offset: 1

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Comments

Numbers k such that floor(k/2) = 4*floor(k/8). - Bruno Berselli, Oct 05 2017

Crossrefs

Union of A008590 and A017077.

Programs

  • Maple
    a[0]:=0:a[1]:=1:for n from 2 to 100 do a[n]:=a[n-2]+8 od: seq(a[n], n=0..58); # Zerinvary Lajos, Mar 16 2008
  • Mathematica
    Riffle[#, # + 1] & [Range[0, 400, 8]] (* Paolo Xausa, Mar 11 2025 *)
  • PARI
    forstep(n=0,200,[1,7],print1(n", ")) \\ Charles R Greathouse IV, Oct 17 2011
    
  • PARI
    a(n) = 4*n - 11/2 - 3*(-1)^n/2; \\ David Lovler, Jul 25 2022
    
  • Python
    def A047393(n): return n-1<<2 if n&1 else (n<<2)-7 # Chai Wah Wu, Mar 11 2025

Formula

a(n) = 8*n - a(n-1) - 15 for n>1, a(1)=0. - Vincenzo Librandi, Aug 05 2010
From R. J. Mathar, Oct 08 2011: (Start)
a(n) = 4*n - 11/2 - 3*(-1)^n/2.
G.f.: x^2*(1+7*x) / ( (1+x)*(x-1)^2 ). (End)
a(n+1) = Sum_{k>=0} A030308(n,k)*A146541(k). - Philippe Deléham, Oct 17 2011
Sum_{n>=2} (-1)^n/a(n) = (sqrt(2)+1)*Pi/16 + log(2)/2 + sqrt(2)*log(sqrt(2)+1)/8. - Amiram Eldar, Dec 18 2021
E.g.f.: ((8*x - 3)*exp(x) + 3*exp(-x))/2 = 4*x*exp(x) - 3*sinh(x). - David Lovler, Aug 02 2022

Extensions

More terms from James Sellers, Jun 20 2000