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A295391
a(1) = 2; a(n+1) = 1 + (a(n)^2 - a(n))*(1+1/n) for n >= 1.
2
2, 5, 31, 1241, 1923551, 4440055831261, 22999778415495431257188671, 604559779613588034852176053517136070371409409780081, 411179093017233901729922229390651516928263091167446329166300037456998815010841080003014976133796409791
OFFSET
1,1
COMMENTS
(a(1), ..., a(n-1), a(n)-1) is an integer solution to the equation Sum_{k=1}^n k/x(k) = 1.
LINKS
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]
FORMULA
a(n) = A275611(n)/A275611(n-1). - N. J. A. Sloane, Sep 03 2024
EXAMPLE
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.
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 *)
CROSSREFS
Closely related to A275611.
Sequence in context: A051399 A080582 A064845 * A259644 A132527 A182327
KEYWORD
nonn
AUTHOR
Robert Israel, Nov 21 2017
STATUS
approved