The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A141345

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A141345

Distance from the n-th highly composite number, A002182(n), to the next prime.
(history; published version)

#19 by N. J. A. Sloane at Fri Dec 25 10:51:38 EST 2020

STATUS

proposed

approved

#18 by A.H.M. Smeets at Thu Dec 24 00:20:28 EST 2020

STATUS

editing

proposed

#17 by A.H.M. Smeets at Thu Dec 24 00:18:40 EST 2020

COMMENTS

The arithmetic mean of a(n)/log(A002182(n)) for the terms 3..10000 is 1.513..., , i.e., a rough approximation is given by a(n) ~ log(A002182(n)^(3/2)). - A.H.M. Smeets, Dec 02 2020

STATUS

proposed

editing

Discussion

Thu Dec 24

00:20

A.H.M. Smeets: Dear Joerg, now I understand what you mean. Indeed, this value must be 1.513, i.e., almost identical. Thanks.

#16 by A.H.M. Smeets at Wed Dec 23 23:59:19 EST 2020

STATUS

editing

proposed

#15 by A.H.M. Smeets at Wed Dec 23 23:58:46 EST 2020

COMMENTS

The arithmetic mean of a(n)/log(A002182(n)) for the terms 3..10000 is 1.513, ..., i.e., a rough approximation is given by a(n) ~ log(A002182(n)^(3/2)). - A.H.M. Smeets, Dec 02 2020

Discussion

Wed Dec 23

23:59

A.H.M. Smeets: Better this way?

#14 by Joerg Arndt at Tue Dec 22 02:49:58 EST 2020

STATUS

proposed

editing

#13 by Michael De Vlieger at Fri Dec 11 17:00:12 EST 2020

STATUS

editing

proposed

Discussion

Tue Dec 22

02:49

Joerg Arndt: the arithmetic mean for all those values is identical?

#12 by Michael De Vlieger at Fri Dec 11 16:59:50 EST 2020

MATHEMATICA

With[{s = Array[DivisorSigma[0, #] &, 10^6]}, Map[NextPrime[#] - # &@ FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]]] (* or *)

Map[NextPrime[#] - # &, Import["https://oeis.org/A002182/b002182.txt", "Data"][[1 ;; 80, -1]] ] (* Michael De Vlieger, Dec 11 2020 *)

STATUS

proposed

editing

#11 by Michel Marcus at Thu Dec 03 00:38:24 EST 2020

STATUS

editing

proposed

#10 by Michel Marcus at Wed Dec 02 16:22:51 EST 2020

COMMENTS

The arithmetic mean of a(n)/log(A002182(n)) for the terms 3..10000 is 1.513, i.e., a rough approximation is given by a(n) ~ log(A002182(n)^(3/2)). _- _A.H.M. Smeets_, Dec 02 2020

STATUS

proposed

editing

Discussion

Wed Dec 02

16:23

Michel Marcus: rather like this

16:52

A.H.M. Smeets: Yes Michel. Thanks!