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A104877
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Semiprimes of the form primorial(n) + 1.
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1
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30031, 9699691, 223092871, 13082761331670031, 117288381359406970983271, 7858321551080267055879091, 40729680599249024150621323471, 267064515689275851355624017992791
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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REFERENCES
| S. M. Ruiz, "A Result on Prime Numbers." Math. Gaz. 81, 269, 1997.
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LINKS
| Eric Weisstein's World of Mathematics, Primorial.
Eric Weisstein's World of Mathematics, Semiprime.
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FORMULA
| n# + 1 iff semiprime. Equals {A002110(i) + 1} intersection {A001358(j)}.
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EXAMPLE
| 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
| 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
| Cf. A001358, A002110, A034386, A005234, A014545, A018239, A006794, A057704, A057705, A104876.
Sequence in context: A138206 A031853 A066576 * A027665 A202598 A113286
Adjacent sequences: A104874 A104875 A104876 * A104878 A104879 A104880
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 28 2005
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