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.

A225156 Denominators of the sequence of fractions f(n) defined recursively by f(1) = 3/1; f(n+1) is chosen so that the sum and the product of the first n terms of the sequence are equal.

Original entry on oeis.org

1, 2, 7, 67, 5623, 37772347, 1653794703916063, 3104205768420613437667191487267, 10767416908549848056705041797805600349527548164015760674541223
Offset: 1

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Author

Martin Renner, Apr 30 2013

Keywords

Comments

Numerators of the sequence of fractions f(n) is A165421(n+1), hence sum(A165421(i+1)/a(i),i=1..n) = product(A165421(i+1)/a(i),i=1..n) = A165421(n+2)/A225163(n) = A011764(n-1)/A225163(n).

Examples

			f(n) = 3, 3/2, 9/7, 81/67, ...
3 + 3/2 = 3 * 3/2 = 9/2; 3 + 3/2 + 9/7 = 3 * 3/2 * 9/7 = 81/14; ...
		

Crossrefs

Programs

  • Maple
    b:=n->3^(2^(n-2)); # n > 1
    b(1):=3;
    p:=proc(n) option remember; p(n-1)*a(n-1); end;
    p(1):=1;
    a:=proc(n) option remember; b(n)-p(n); end;
    a(1):=1;
    seq(a(i),i=1..9);

Formula

a(n) = 3^(2^(n-2)) - product(a(i),i=1..n-1), n > 1 and a(1) = 1.
a(n) = 3^(2^(n-2)) - p(n) with a(1) = 1 and p(n) = p(n-1)*a(n-1) with p(1) = 1.