A377229 -id:A377229 - cp's OEIS frontend

A377205 Lexicographically earliest sequence of positive integers a(1), a(2), ... such that for any n >= 0, s(n) = Sum_{k=1..n} 1/(k^2*a(k)) < 1.

2, 1, 1, 1, 1, 1, 3, 9, 171, 122014, 17661589931, 412924014578486602517, 1248808068140660770289141544749321839183623, 4529027355107615424925871833487047912228337079416162414871862143803627237910792872226

Offset: 1

Alois P. Heinz, Oct 19 2024

nonn

			s(0), s(1), ... = 0, 1/2, 3/4, 31/36, 133/144, 3469/3600, 3569/3600, ... .

Alois P. Heinz, Table of n, a(n) for n = 1..17

Cf. A000290, A013661, A374663, A377229, A377230.

s:= proc(n) option remember; `if`(n=0, 0, s(n-1)+1/(n^2*a(n))) end:
a:= proc(n) option remember; 1+floor(1/((1-s(n-1))*n^2)) end:
seq(a(n), n=1..14);

A377230 Lexicographically earliest sequence of positive integers a(1), a(2), ... such that for any n >= 0, s(n) = Sum_{k=1..n} 1/(T(k)*a(k)) < 1, T = A000217.

Original entry on oeis.org

2, 1, 2, 2, 3, 5, 23, 806, 519065, 220441054222, 222723684271305542570701, 41974171914555858099300698444579076459265512901, 1510140949639448391630842209382251970116940997822995817347241840058937174456186756365141648201

Offset: 1

Alois P. Heinz, Oct 20 2024

nonn

			s(0), s(1), ... = 0, 1/2, 5/6, 11/12, 29/30, 89/90, 629/630, ... .

Alois P. Heinz, Table of n, a(n) for n = 1..16

Cf. A000217, A374663, A377205, A377229.

T:= n-> n*(n+1)/2:
s:= proc(n) option remember; `if`(n=0, 0, s(n-1)+1/(T(n)*a(n))) end:
a:= proc(n) option remember; 1+floor(1/((1-s(n-1))*T(n))) end:
seq(a(n), n=1..13);

cp's OEIS Frontend

A377205 Lexicographically earliest sequence of positive integers a(1), a(2), ... such that for any n >= 0, s(n) = Sum_{k=1..n} 1/(k^2*a(k)) < 1.

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