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Search: id:A108894
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| A108894 |
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Numbers n such that (n!/n#) * 2^n + 1 is prime, where n# = primorial numbers (A034386). |
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+0
2
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| 0, 1, 2, 11, 17, 25, 38, 53, 107, 245, 255, 367, 719, 1077, 2189, 2853, 3236, 3511, 3633, 4531, 4858, 5422
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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n!/n# is known as n compositorial. All values have been proved prime. No more terms up to 6100. Primality proof for the largest, which has 17219 digits: PFGW Version 1.2.0 for Windows [FFT v23.8] Primality testing (5422!/5422#)*(2^5422)+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2719 Calling Brillhart-Lehmer-Selfridge with factored part 36.34% (5422!/5422#)*(2^5422)+1 is prime! (66.5095s+0.0129s)
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MATHEMATICA
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f[n_] := n!/Fold[Times, 1, Prime[ Range[ PrimePi[ n]]]]*2^n + 1; Do[ If[ PrimeQ[ f[n]], Print[n]], {n, 0, 1100}] (from Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 18 2005)
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CROSSREFS
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Cf. A049420, A091421.
Sequence in context: A156829 A105840 A060427 this_sequence A066794 A153222 A087379
Adjacent sequences: A108891 A108892 A108893 this_sequence A108895 A108896 A108897
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KEYWORD
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more,nonn
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AUTHOR
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Jason Earls (zevi_35711(AT)yahoo.com), Jul 15 2005
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