A376184 Lexicographically earliest sequence of positive integers a(1), a(2), a(3), ... such that for any n > 0, S(n) = Sum_{k = 1..n} b(k)/a(k) < 1, where {b(k)} is the sequence b(1)=5/4, b(2*i)=3/2, b(2*i+1)=6/5 (i>0).

2, 5, 17, 341, 92753, 10753782821, 92515075960384748177, 10698799099944699918936107506299150093941, 91571441744782016867976366392607084634231243149599342901251284090792487979854033

Offset

1,1

Comments

This sequence and A376062 were discovered by Rémy Sigrist on Sep 09 2024. The two sequences {b(1)=7/6, b(k)=5/4 for k>1} and {b(1)=5/4, b(2*k)=3/2, b(2*k+1)=6/5 for k>0} are the first sequences {b(i)} discovered with the property that the sums S(n) do not converge to numbers of the form (e_n - 1)/e_n as n-> oo.

Links

Table of n, a(n) for n=1..9.

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]

Example

The initial values of S(n) are 5/8, 37/40, 677/680, 231877/231880, 21507565637/21507565640, 231287689900961870437/231287689900961870440, ...

Crossrefs

Cf. A004168, A082732, A374663, A375516, A375531, A375532, A375781, A375522, A376048-A376062, A376186.

Sequence in context: A269835 A111635 A041455 * A348927 A081465 A128000

Adjacent sequences: A376181 A376182 A376183 * A376185 A376186 A376187

Keyword

nonn,base

Author

N. J. A. Sloane, Sep 15 2024.

Status

approved