A377230 -id:A377230 - 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);

A377229 Lexicographically earliest sequence of positive integers a(1), a(2), ... such that for any n >= 0, s(n) = Sum_{k=1..n} 1/(F(k)*a(k)) < 1, F = Fibonacci.

Original entry on oeis.org

2, 3, 4, 9, 44, 1486, 1357976, 1855074754595, 2975714380792664939835466, 46528348836004781630107949818181021469921360198769

Offset: 1

Alois P. Heinz, Oct 20 2024

nonn

			s(0), s(1), ... = 0, 1/2, 5/6, 23/24, 215/216, 11879/11880, 17653679/17653680, ... .

Alois P. Heinz, Table of n, a(n) for n = 1..14

Cf. A000045, A079586, A374663, A376058, A377205, A377230.

F:= combinat[fibonacci]:
s:= proc(n) option remember; `if`(n=0, 0, s(n-1)+1/(F(n)*a(n))) end:
a:= proc(n) option remember; 1+floor(1/((1-s(n-1))*F(n))) end:
seq(a(n), n=1..11);

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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