The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A030003 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A030003

(prime(n)-3)(prime(n)-5)(prime(n)-7)/48.
(history; published version)

#11 by Harvey P. Dale at Wed Jul 10 12:53:44 EDT 2024

STATUS

editing

approved

#10 by Harvey P. Dale at Wed Jul 10 12:53:42 EDT 2024

MATHEMATICA

((#-3)(#-5)(#-7))/48&/@Prime[Range[2, 50]] (* Harvey P. Dale, Jul 10 2024 *)

STATUS

approved

editing

#9 by Charles R Greathouse IV at Sun Aug 03 14:01:15 EDT 2014

MATHEMATICA

Table[(p - 3) (p - 5) (p - 7)/48, {p, Prime[Range[2, 50]]}] (* _T. D. Noe, _, Apr 16 2012 *)

Discussion

Sun Aug 03

14:01

OEIS Server: https://oeis.org/edit/global/2267

#8 by T. D. Noe at Mon Apr 16 13:18:11 EDT 2012

STATUS

editing

approved

#7 by T. D. Noe at Mon Apr 16 13:17:26 EDT 2012

NAME

(pprime(n)-3)(pprime(n)-5)(pprime(n)-7)/48, as p runs through primes.

OFFSET

3,2,4

LINKS

T. D. Noe, <a href="/A030003/b030003.txt">Table of n, a(n) for n = 2..1000</a>

#6 by T. D. Noe at Mon Apr 16 13:12:14 EDT 2012

DATA

0, 0, 0, 4, 10, 35, 56, 120, 286, 364, 680, 969, 1140, 1540, 2300, 3276, 3654, 4960, 5984, 6545, 8436, 9880, 12341, 16215, 18424, 19600, 22100, 23426, 26235, 37820, 41664, 47905, 50116, 62196, 64824, 73150, 82160, 88560, 98770, 109736, 113564, 134044, 138415

COMMENTS

It appears that a(n) is a subset of binomial(f(n),3) where f(n)=floor((3*n-7)/3). - Gary Detlefs, Apr 14 2012

MATHEMATICA

Table[(p - 3) (p - 5) (p - 7)/48, {p, Prime[Range[2, 50]]}] (* T. D. Noe, Apr 16 2012 *)

STATUS

proposed

editing

#5 by Gary Detlefs at Sat Apr 14 15:05:42 EDT 2012

STATUS

editing

proposed

Discussion

Sat Apr 14

15:36

Charles R Greathouse IV: Perhaps we should add a zero and change the offset to 1?

20:37

Charles R Greathouse IV: floor((3*n-7)/3) = n - 3 for any integer n, so binomial(f(n),3) = (n-3)(n-4)(n-5)/6. This equals (p-3)(p-5)(p-7)/48 when n = (p+3)/2.

#4 by Gary Detlefs at Sat Apr 14 15:01:18 EDT 2012

COMMENTS

It appears that a(n) is a subset of binomial(f(n),3) where f(n)=floor((3*n-7)/3)-Gary Detlefs, Apr 14 2012

STATUS

approved

editing

Discussion

Sat Apr 14

15:05

Gary Detlefs: I am unclear as to why this sequence begins with 3 zeros. If I run the code (p-3)*(p-5)*(p-7)/48 in Maple (using ithprime(n) for p), from offset 3, I obtain a sequence with only 2 starting zeros.

#3 by Russ Cox at Fri Mar 30 16:47:16 EDT 2012

AUTHOR

_N. J. A. Sloane (njas(AT)research.att.com)_.

Discussion

Fri Mar 30

16:47

OEIS Server: https://oeis.org/edit/global/110

#2 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

KEYWORD

nonn,new

nonn

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).