The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A375522 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A375522

a(n) is the denominator of Sum_{k = 1..n} 1 / (k*A375781(k)).
(history; published version)

#21 by N. J. A. Sloane at Sun Oct 20 23:41:36 EDT 2024

STATUS

editing

approved

#20 by N. J. A. Sloane at Sun Oct 20 23:41:34 EDT 2024

LINKS

N. J. A. Sloane, <a href="https://www.youtube.com/watch?v=3RAYoaKMckM">A Nasty Surprise in a Sequence and Other OEIS Stories</a>, Experimental Mathematics Seminar, Rutgers University, Oct 10 2024, Youtube video; <a href="https://sites.math.rutgers.edu/~zeilberg/expmath/sloane85BD.pdf">Slides</a> [Mentions this sequence]

STATUS

approved

editing

#19 by OEIS Server at Fri Oct 18 18:38:05 EDT 2024

LINKS

Alois P. Heinz, <a href="/A375522/b375522_1.txt">Table of n, a(n) for n = 0..13</a>

#18 by Alois P. Heinz at Fri Oct 18 18:38:05 EDT 2024

STATUS

editing

approved

Discussion

Fri Oct 18

18:38

OEIS Server: Installed first b-file as b375522.txt.

#17 by Alois P. Heinz at Fri Oct 18 18:38:01 EDT 2024

LINKS

Alois P. Heinz, <a href="/A375522/b375522_1.txt">Table of n, a(n) for n = 0..13</a>

#16 by Alois P. Heinz at Fri Oct 18 18:36:36 EDT 2024

MAPLE

s:= proc(n) s(n):= `if`(n=0, 0, s(n-1)+1/(ithprime(n)*b(n))) end:

b:= proc(n) b(n):= 1+floor(1/((1-s(n-1))*ithprime(n))) end:

a:= n-> denom(s(n)):

seq(a(n), n=0..10); # Alois P. Heinz, Oct 18 2024

#15 by Alois P. Heinz at Fri Oct 18 18:36:04 EDT 2024

DATA

1, 2, 6, 15, 105, 1155, 1336335, 892896284280, 398631887241408183843480, 19863422690705846097977473796903171171326157280, 14091270035344566960604487534521565339065390839583445590118556137472614250693240040301050080

OFFSET

1,1

0,2

EXAMPLE

The first few fractions are 0/1, 1/2, 5/6, 14/15, 103/105, 1154/1155, 1336333/1336335, 892896284279/892896284280, ...

EXTENSIONS

a(0)=1 prepended by Alois P. Heinz, Oct 18 2024

STATUS

approved

editing

#14 by N. J. A. Sloane at Sat Aug 31 21:24:50 EDT 2024

STATUS

editing

approved

#13 by N. J. A. Sloane at Sat Aug 31 21:24:48 EDT 2024

COMMENTS

The differences S2(n) - S1(n) are surprisingly small: _Rémy Sigrist_ finds that for n = 1,2,...,34 the values S2(n) - S1(n) are:

STATUS

approved

editing

#12 by N. J. A. Sloane at Sat Aug 31 21:20:57 EDT 2024

STATUS

editing

approved