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.

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A330806 a(1) = 1; a(2) = 1; for n >= 3, a(n) = a(n-1) / gcd(a(n-1), n-1) + a(n-2) / gcd(a(n-2), n-2).

Original entry on oeis.org

1, 1, 2, 3, 5, 4, 3, 5, 8, 13, 21, 34, 38, 55, 93, 86, 74, 117, 87, 100, 92, 97, 189, 286, 332, 475, 807, 744, 455, 641, 1096, 1737, 2833, 4570, 5118, 7403, 12521, 19924, 22483, 32445, 28972, 35461, 64433, 99894, 114380, 72823, 95699, 168522, 123786, 151873
Offset: 1

Views

Author

Ctibor O. Zizka, Jan 01 2020

Keywords

Comments

2 >= a(n) / a(n-1) > 0. Empirically the average growth rate is 1.32... in comparison to 1.618... (golden ratio).
a(n)^(1/n) tends to 1.228... - Vaclav Kotesovec, Jan 01 2020

Examples

			a(1) = 1; a(2) = 1; a(3) = 1/gcd(1,2) + 1/gcd(1,1) = 2; a(4) = 2/gcd(2,3) + 1/gcd(1,2) = 3 and so on.
		

Crossrefs

Programs

  • Magma
    a:=[1,1]; for n in [3..60] do Append(~a,a[n-1]/ Gcd(a[n-1], n-1) + a[n-2] / Gcd(a[n-2], n-2)); end for; a; // Marius A. Burtea, Jan 01 2020
    
  • Mathematica
    a[1] = a[2] = 1; a[n_] := a[n] = a[n - 1] / GCD[a[n - 1], n - 1] + a[n - 2] / GCD[a[n - 2], n - 2]; Array[a, 100] (* Amiram Eldar, Jan 01 2020 *)
  • PARI
    seq(n)={my(a=vector(n)); a[1]=a[2]=1; for(n=3, #a, a[n] = a[n-1]/gcd(a[n-1], n-1) + a[n-2]/gcd(a[n-2], n-2)); a} \\ Andrew Howroyd, Jan 01 2020
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