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 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 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[#]-#[]#[])&/@Partition[Prime[Range], 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

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