A375530 - OEIS

%I #22 Oct 21 2024 11:23:31

%S 1,3,30,4530,143650830,226991170700228730,

%T 669824890486184912549321336826596430,

%U 7627311526552103393330686732733999706332372434754669475019405844335259730

%N a(n) is the denominator of Sum_{k = 1..n} prime(k) / A375529(k).

%H Alois P. Heinz, <a href="/A375530/b375530.txt">Table of n, a(n) for n = 0..11</a>

%H N. J. A. Sloane, <a href="https://www.youtube.com/watch?v=3RAYoaKMckM">A Nasty Surprise in a Sequence and Other OEIS Stories</a>, Experimental Mathematics Seminar, Rutgers University, Oct 10 2024, Youtube video; <a href="https://sites.math.rutgers.edu/~zeilberg/expmath/sloane85BD.pdf">Slides</a> [Mentions this sequence]

%F a(n) = prime(n)*a(n-1)^2 + a(n-1), with a(0) = 1.

%e The first few fractions Sum_{k = 1..n} prime(k) / A375529(k) are 0/1, 2/3, 29/30, 4529/4530, 143650829/143650830, 226991170700228729/226991170700228730, ...

%p a:= proc(n) option remember; `if`(n=0, 1,

%p       ithprime(n)*a(n-1)^2+a(n-1))

%p     end:

%p seq(a(n), n=0..7);  # _Alois P. Heinz_, Oct 21 2024

%Y Cf. A374663, A374983/A375516, A375529.

%K nonn,frac

%O 0,2

%A _Rémy Sigrist_ and _N. J. A. Sloane_, Sep 04 2024

%E a(0)=1 prepended by _Alois P. Heinz_, Oct 21 2024