login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A117301 Prime(n+3)*prime(n) - prime(n+1)*prime(n+2). 10
-1, -2, -12, -24, -12, -24, 56, -78, -48, 42, -184, -24, 152, 46, -260, -48, 102, -304, 110, 126, -60, 276, -250, -630, -24, -12, -24, 1272, -72, -1156, -294, 476, -24, -676, 580, -374, -60, 286, -740, 644, -24, -1206, -12, 1520, 1942, -1880 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The number of negative values in this sequence appears to be consistently larger than the number of positive values. The following list gives the number of positive terms among the first n terms divided through the number of negative terms among the first n terms for various n.

n ratio

10^2 0.51515151515...

10^3 0.70940170940...

10^4 0.80212650928...

10^5 0.83826908582...

10^6 0.86339454584...

Cino Hilliard conjectures that this ratio converges and that there are infinitely many elements in the sequence whose absolute value is 12.

It appears that the positions of negative multiples of 12 in A117301 are given by A064026(n+1) for n>=1.  If so, then Hilliard's conjecture is true, and a further conjecture is that if k>=2 then there are infinitely multiples of -12*k in A117301. - Clark Kimberling, Jan 01 2014

LINKS

Table of n, a(n) for n=1..46.

FORMULA

a(n) = A090090(n) - A006094(n+1). - Michel Marcus, Oct 07 2013

EXAMPLE

a(4) = prime(4)*prime(7) - prime(5)*prime(6) = 7*17 - 11*13 = -24.

MATHEMATICA

Table[Prime[n]*Prime[n + 3] - Prime[n + 1]Prime[n + 2], {n, 1, 100}] (* Stefan Steinerberger, Jun 27 2007 *)

(* The following program is significantly faster: *)

(First[#]Last[#]-#[[2]]#[[3]])&/@Partition[Prime[Range[50]], 4, 1] (* Harvey P. Dale, May 08 2011 *)

PROG

(PARI) det2cont(n) = {local(m, p, x, D); m=0; p=0; for(x=1, n, D=prime(x)*prime(x+3)-prime(x+1)*prime(x+2); if(D<0, m++, p++); print1(D", ") ); print(); print("neg= "m); print("pos= "p); print("pos/neg = "p/m+.) }

CROSSREFS

Sequence in context: A009514 A192851 A112718 * A141079 A269841 A144551

Adjacent sequences:  A117298 A117299 A117300 * A117302 A117303 A117304

KEYWORD

sign

AUTHOR

Cino Hilliard, Apr 24 2006

EXTENSIONS

Edited by Stefan Steinerberger, Jun 27 2007

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 25 23:17 EDT 2020. Contains 338026 sequences. (Running on oeis4.)