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A117027
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Determinants of 2 X 2 matrices of non-overlapping blocks of 4 consecutive primes.
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1
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-1, -12, -48, 152, 102, -60, -24, -72, -24, -60, -24, 1942, 896, -1124, 522, -1938, 554, 1376, -806, -96, -24, 1716, 4598, -48, 2886, -2348, -96, 2380, 4908, 1246, -4158, -180, -1526, 1442, -1882, -4986, -5214, -72, -96, -5694, -2014, -84, -2058, 8232, -4324, -24, -84, -14076, -4844, -7398, 12274
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The terminology "non-overlapping" is used to distinguish from "continuous" which would be block 1: 2, 3, 5, 7; block 2: 3, 5, 7, 11 etc.
The number of negative values in this sequence appears to be consistently
larger than the number of positive values. For n=10^x we have ratios:
n ratio pos/neg first difference of ratio:
10^2 0.66666666666...
10^3 0.61290322580... -0.053
10^4 0.76928520877... 0.156
10^5 0.83163601729... 0.062
10^6 0.85985612153... 0.028
This suggests the ratio is approaching a limit close to 0.87.
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FORMULA
| a(n) = prime(4n-3)*prime(4n)-prime(4n-2)*prime(4n-1).
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EXAMPLE
| The 4th block of 4-primes is 41,43,47,53. So the determinant is = 41*53 - 43*47 = 152 = a(4).
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MAPLE
| A117027 := proc(n) ithprime(4*n-3)*ithprime(4*n)-ithprime(4*n-2)*ithprime(4*n-1) ; end proc:
seq(A117027(n), n=1..30) ; # R. J. Mathar, Mar 27 2010
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PROG
| (PARI) det(n) = {local(m, p, x, D); m=0; p=0;
forstep(x=1, n, 4, 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: A006564 A059162 A190622 * A161171 A007200 A061148
Adjacent sequences: A117024 A117025 A117026 * A117028 A117029 A117030
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KEYWORD
| sign,easy
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AUTHOR
| Cino Hilliard (hillcino368(AT)gmail.com), Apr 24 2006
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EXTENSIONS
| Formula reformulated using standard nomenclature - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 27 2010
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