A375530 a(n) is the denominator of Sum_{k = 1..n} prime(k) / A375529(k).

1, 3, 30, 4530, 143650830, 226991170700228730, 669824890486184912549321336826596430, 7627311526552103393330686732733999706332372434754669475019405844335259730

Offset: 0

Author

Rémy Sigrist and N. J. A. Sloane, Sep 04 2024

Keywords

• nonn
• frac

Examples

			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, ...
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..11
• 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

Cf. A374663, A374983/A375516, A375529.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1,
      ithprime(n)*a(n-1)^2+a(n-1))
    end:
seq(a(n), n=0..7);  # Alois P. Heinz, Oct 21 2024

Formula

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

Extensions

a(0)=1 prepended by Alois P. Heinz, Oct 21 2024