

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
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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



