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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. 2
1, 2, 7, 67, 5623, 37772347, 1653794703916063, 3104205768420613437667191487267, 10767416908549848056705041797805600349527548164015760674541223 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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).

LINKS

Table of n, a(n) for n=1..9.

Paul Yiu, Recreational Mathematics, Department of Mathematics, Florida Atlantic University, 2003, Chapter 5.4,  p. 207 (Project).

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.

EXAMPLE

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; ...

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);

CROSSREFS

Cf. A011764, A100441, A165421, A225163.

Sequence in context: A099660 A207978 A307246 * A260968 A322223 A173226

Adjacent sequences:  A225153 A225154 A225155 * A225157 A225158 A225159

KEYWORD

nonn,frac

AUTHOR

Martin Renner, Apr 30 2013

STATUS

approved

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Last modified June 17 17:41 EDT 2019. Contains 324196 sequences. (Running on oeis4.)