The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A248912 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A248912

a(n) = floor(prime(n) - (n+1)*(log(n) + log(log(n))) + n) for n > 1.
(history; published version)

#19 by Michael De Vlieger at Sat Mar 05 14:16:54 EST 2022

STATUS

proposed

approved

#18 by Jon E. Schoenfield at Sat Mar 05 13:32:32 EST 2022

STATUS

editing

proposed

Discussion

Sat Mar 05

14:16

Michael De Vlieger: Checked Mathematica; generates terms.

#17 by Jon E. Schoenfield at Sat Mar 05 13:26:17 EST 2022

NAME

a(n) = floor(prime(n) - (n+1)*(log(n) + log(log(n))) + n) for n > 1.

COMMENTS

See A059112 for floor( prime(n) - n*log(n) - n*log(log(n)) + n ) where prime(n) is the n-th prime.

EXAMPLE

a(8) = 1 because floor(prime(8)-(8+1)*(log(8)+log(log(8))) + 8) = floor(19-9*(2.0794415...+0.7320993...) + 8) = floor(1.6961318...) = 1.

PROG

(MAGMAMagma) [Floor((NthPrime(n)-(n+1)*(Log(n)+Log(Log(n)))+n)): n in [2..80]]; // Vincenzo Librandi, Oct 16 2014

STATUS

proposed

editing

Discussion

Sat Mar 05

13:32

Jon E. Schoenfield: Unless I’ve overlooked something, the parentheses in the Name, Example, and programs seem to agree (although the Maple is a little different, but seems equivalent). I was going to try running the Magma program on the Online Magma Calculator, but every time I try to go there (am using my phone), I get an error message saying that the server cannot be found.

#16 by Michel Marcus at Sat Mar 05 12:18:18 EST 2022

STATUS

editing

proposed

#15 by Michel Marcus at Sat Mar 05 12:17:09 EST 2022

NAME

a(n) = floor( prime(n)-(n+1)*(log(n)+log(log(n))) + n ) for n>1.

EXAMPLE

a(8) = 1 because floor(prime(8)-(8+1)*(log(8)+log(log(8))) + 8) = floor(19-9*(2.0794415...+.7320993...)+ 8) = floor(1.6961318...) = 1.

PROG

(PARI) a(n) = floor(prime(n)-(n+1)*(log(n)+log(log(n))) + n); \\ Michel Marcus, Mar 05 2022

Discussion

Sat Mar 05

12:18

Michel Marcus: I have been obliged to add a right parenthesis to name and example; can someone check them and programs too; thanks

#14 by Michel Marcus at Sat Mar 05 12:10:08 EST 2022

COMMENTS

See A059112 for floor( pprime(n) - n*log(n) - n*log(log(n)) + n ) where pprime(n) is n-th prime.

STATUS

approved

editing

#13 by Michel Marcus at Tue Jun 23 00:52:17 EDT 2015

STATUS

reviewed

approved

#12 by Wesley Ivan Hurt at Mon Jun 22 22:55:50 EDT 2015

STATUS

proposed

reviewed

#11 by Jon E. Schoenfield at Mon Jun 22 22:53:31 EDT 2015

STATUS

editing

proposed

#10 by Jon E. Schoenfield at Mon Jun 22 22:53:28 EDT 2015

COMMENTS

See A059112 for floor( p(n) - n*lnlog(n) - n*lnlog(lnlog(n)) + n ) where p(n) is n-th prime.

STATUS

approved

editing