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Search: id:A104877
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| A104877 |
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Semiprimes of the form primorial(n) + 1. |
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+0
2
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| 30031, 9699691, 223092871, 13082761331670031, 117288381359406970983271, 7858321551080267055879091, 40729680599249024150621323471, 267064515689275851355624017992791
(list; graph; listen)
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OFFSET
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0,1
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REFERENCES
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S. M. Ruiz, "A Result on Prime Numbers." Math. Gaz. 81, 269, 1997.
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LINKS
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Eric Weisstein's World of Mathematics, Primorial.
Eric Weisstein's World of Mathematics, Semiprime.
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FORMULA
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n# + 1 iff semiprime. Equals {A002110(i) + 1} intersection {A001358(j)}.
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EXAMPLE
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6# + 1 = 2*3*5*7*11*13 + 1 = 30031 = 59 x 509.
8# + 1 = 2*3*5*7*11*13*17*19 + 1 = 9699691 = 347 x 27953.
9# + 1 = 2*3*5*7*11*13*17*19*23 + 1 = 223092871 = 317 x 703763.
14# + 1 = 2*3*5*7*11*13*17*19*23*29*31*37*41*43 + 1 = 13082761331670031 = 167 x 78339888213593.
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MATHEMATICA
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From Ray Chandler: Bigomega[n_]:=Plus@@Last/@FactorInteger[n]; SemiprimeQ[n_]:=Bigomega[n]?2; Primorial[n_]:=Product[Prime[i], {i, n}]; Select[Table[Primorial[n]+1, {n, 30}], SemiprimeQ]
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CROSSREFS
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Cf. A001358, A002110, A034386, A005234, A014545, A018239, A006794, A057704, A057705, A104876.
Sequence in context: A138206 A031853 A066576 this_sequence A027665 A113286 A027687
Adjacent sequences: A104874 A104875 A104876 this_sequence A104878 A104879 A104880
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 28 2005
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