A295391 a(1) = 2; a(n+1) = 1 + (a(n)^2 - a(n))*(1+1/n) for n >= 1.

2, 5, 31, 1241, 1923551, 4440055831261, 22999778415495431257188671, 604559779613588034852176053517136070371409409780081, 411179093017233901729922229390651516928263091167446329166300037456998815010841080003014976133796409791

Offset: 1

Author

Robert Israel, Nov 21 2017

Keywords

• nonn

Comments

(a(1), ..., a(n-1), a(n)-1) is an integer solution to the equation Sum_{k=1}^n k/x(k) = 1.

Examples

			1/1 = 1.
1/2 + 2/4 = 1.
1/2 + 2/5 + 3/30 = 1.
1/2 + 2/5 + 3/31 + 4/1240 = 1.
1/2 + 2/5 + 3/31 + 4/1241 + 5/1923550 = 1.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..12
• R. Israel, Set of solutions to a sum, Mathematics StackExchange.
• N. J. A. Sloane, A Nasty Surprise in a Sequence and Other OEIS Stories, Experimental Mathematics Seminar, Rutgers University, Oct 10 2024, Youtube video; Slides [Mentions this sequence]

Crossrefs

Closely related to A275611.

Programs

Maple

a[1]:= 2:
for n from 1 to 10 do a[n+1]:= 1 + (a[n]^2 - a[n])*(1+1/n) od:
seq(a[i],i=1..11);

Mathematica

Fold[Append[#1, 1 + (Last[#1]^2 - Last[#1]) (1 + 1/#2)] &, {2}, Range@ 8] (* Michael De Vlieger, Nov 21 2017 *)

Formula

a(n) = A275611(n)/A275611(n-1). - N. J. A. Sloane, Sep 03 2024