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A376043

a(1)=1; thereafter a(n) = smallest positive integer such that Sum_{i=2..n} a(i-1)/a(i) is less than 1.

1, 2, 5, 51, 26011, 345051781711, 1579413237848133436283359452811, 11418342003878959546444158608577711406460297342648955785594970237449922006239911

OFFSET

1,2

LINKS

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(1)=1; for n>1, a(n) = a(n-1)*A376044(n-2) + 1.

More directly, a(1) = 1; thereafter a(n) = 1 + a(n-1) * Prod_{i=1..n-1} a(i). - N. J. A. Sloane, Sep 12 2024

MAPLE

# To get M terms of A376043 and A376044:

a:=Array(0..100, 0): b:=Array(0..100, 0): e:=Array(0..100, 0):

e[0]:=1; a[0]:=1; e[1]:=2; b[1]:=1; a[1]:=2;

M:=8;

for n from 2 to M do

b[n]:=a[n-1];

e[n]:=e[n-1]*(b[n]*e[n-1]+1);

a[n]:=b[n]*e[n-1]+1;

od:

[seq(b[n], n=1..M)]; # this sequence

[seq(e[n], n=1..M)]; # A376044

MATHEMATICA

a[1] = 1; a[n_] := a[n] = 1 + Floor[a[n-1]/(1 - Sum[a[i-1]/a[i], {i, 2, n-1}])]; Array[a, 8] (* Amiram Eldar, Sep 08 2024 *)

CROSSREFS

KEYWORD

nonn

AUTHOR

STATUS

approved

URL: https://oeis.org/A376043