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Search: id:A100595
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| A100595 |
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Numbers n such that (prime(n)-1)! + prime(n)^9 is prime. |
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1
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OFFSET
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1,1
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COMMENT
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There are no more such n up to n=150. Computed in collaboration with Ray Chandler.
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FORMULA
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Numbers n such that (prime(n)-1)! + prime(n)^9 is prime, where prime(n) is the n-th prime.
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EXAMPLE
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a(1) = 9 because (prime(9)-1)! + prime(9)^9 = (23-1)! + 23^9 = 1124000729578760341463 is the smallest prime of this form.
a(2) = 10 because (prime(10)-1)! + prime(10)^9 = (29-1)! + 29^9 = 304888344611713875008649975869 is the 2nd smallest prime of this form.
a(3) = 17, but prime(17) = 59 yields a number that would take 2 full lines of this page; and a(4) = 137 because prime(137) = 773 yields a prime of this form which is 1975 digits long. Note also that 773 = prime(137) = prime(prime(34)).
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MATHEMATICA
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lst={}; Do[p=Prime[n]; If[PrimeQ[(p-1)!+p^9], AppendTo[lst, n]], {n, 12^2}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 08 2008]
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CROSSREFS
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Cf. A100858.
Sequence in context: A106690 A045568 A088036 this_sequence A107433 A090570 A131417
Adjacent sequences: A100592 A100593 A100594 this_sequence A100596 A100597 A100598
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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), Nov 30 2004
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