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A117301
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Prime(n+3)*prime(n) - prime(n+1)*prime(n+2).
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9
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-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; internal format)
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OFFSET
| 1,2
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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.
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EXAMPLE
| a(4) = prime(4)*prime(7) - prime(5)*prime(6) = 7*17 - 11*13 = -24
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MATHEMATICA
| Table[Prime[n]*Prime[n + 3] - Prime[n + 1]Prime[n + 2], {n, 1, 100}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com, Jun 27 2007
(* The following program is significantly faster: *)
(First[#]Last[#]-#[[2]]#[[3]])&/@Partition[Prime[Range[50]], 4, 1] (* From Harvey P. Dale, May 08 2011 *)
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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+.) }
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CROSSREFS
| Sequence in context: A009514 A192851 A112718 * A141079 A144551 A174457
Adjacent sequences: A117298 A117299 A117300 * A117302 A117303 A117304
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KEYWORD
| sign
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AUTHOR
| Cino Hilliard (hillcino368(AT)gmail.com), Apr 24 2006
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EXTENSIONS
| Edited by Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Jun 27 2007
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