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Search: id:A080469
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| A080469 |
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Composite n such that binomial(3*n,n)==3^n (mod n). |
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+0
5
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| 36, 57, 121, 132, 552, 8397, 7000713, 9692541, 36294723, 564033861
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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If p is prime, binomial(3*p,p)==3^p (mod p)
No other terms below 10^9.
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LINKS
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Max Alekseyev, PARI scripts for various problems
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EXAMPLE
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57 is a term because binomial(3*57, 57) = 12039059761216294940321619222324879408784636200 mod 57 = 27 == 3^57 mod 57.
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MATHEMATICA
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Do[If[ !PrimeQ[n], k = Binomial[3*n, n]; m = 3^n; If[Mod[k, n] == Mod[m, n], Print[n]]], {n, 1, 70000}] (Propper)
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CROSSREFS
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Cf. A109641, A109642.
Sequence in context: A050691 A124941 A116321 this_sequence A066505 A039419 A043242
Adjacent sequences: A080466 A080467 A080468 this_sequence A080470 A080471 A080472
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KEYWORD
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nonn,more,hard,new
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 15 2003
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EXTENSIONS
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One more term from Ryan Propper (rpropper(AT)stanford.edu), Aug 12 2005
Four new terms added by Max Alekseyev (maxale(AT)gmail.com), Nov 05 2009
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