The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A211280

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A211280

Numerator of prime(n+1) - prime(n)/2.
(history; published version)

#24 by R. J. Mathar at Tue Nov 07 08:22:42 EST 2023

STATUS

editing

approved

#23 by R. J. Mathar at Tue Nov 07 08:21:27 EST 2023

COMMENTS

The list of denominators is 1, 2, 2, ... (2 repeated), so a(n) = A210497(n) for n>1.

STATUS

approved

editing

#22 by Harvey P. Dale at Sun Mar 05 13:20:57 EST 2023

STATUS

editing

approved

#21 by Harvey P. Dale at Sun Mar 05 13:20:54 EST 2023

MATHEMATICA

Numerator[#[[2]]-#[[1]]/2]&/@Partition[Prime[Range[80]], 2, 1] (* Harvey P. Dale, Mar 05 2023 *)

STATUS

approved

editing

#20 by R. J. Mathar at Tue Jul 10 14:43:11 EDT 2012

STATUS

editing

approved

#19 by R. J. Mathar at Tue Jul 10 14:41:55 EDT 2012

COMMENTS

Doubled or triplicated successive terms 15,15, 21,21, 45,45, 75,75, 105,105,105, 111,111, .. are multiples of 3.

a(n) - prime(n) = 2*prime(n+1)-prime(n)-prime(n) are two times prime differences, (A001223, ) multiplied by 2, and therefore multiples of 4.

FORMULA

a(n) = prime(n+2) - A036263(n), n>1. - R. J. Mathar, Jul 10 2012

STATUS

proposed

editing

Discussion

Tue Jul 10

14:43

R. J. Mathar: The claim on divisibility by 3 for repeated terms was incorrect (at n = 242, 290 etc).

#18 by Charles R Greathouse IV at Tue Jul 10 12:55:25 EDT 2012

STATUS

editing

proposed

#17 by Charles R Greathouse IV at Tue Jul 10 12:55:05 EDT 2012

COMMENTS

The list of denominators is 1, 2, 2, .. . (2 repeated).

FORMULA

a(n) ~ n log n. Apart from the first term, a(n) = 2*prime(n+1) - prime(n). - Charles R Greathouse IV, Jul 10 2012

CROSSREFS

Denominators are A040000.

STATUS

proposed

editing

Discussion

Tue Jul 10

12:55

Charles R Greathouse IV: I don't really see the interest, but OK.

#16 by R. J. Mathar at Tue Jul 10 12:48:56 EDT 2012

STATUS

editing

proposed

#15 by R. J. Mathar at Tue Jul 10 12:48:51 EDT 2012

COMMENTS

The list of denominators is 1, 2, 2, .. (2 repeated).

a(n) - prime(n) = 2*prime(n+1)-prime(n)-prime(n) are two times prime differences, A001223, and therefore, with one exception, multiples of 4.