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Search: id:A095189
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| A095189 |
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Smallest prime formed by the digit string after decimal point of n^(1/n), or 0 if no such prime exists. |
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+0
1
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| 0, 41, 442249570307408382321638310780109588391, 41, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 19, 189207115002721, 181, 17, 167, 16158634964154228180872122424567684345543663819, 15601, 15085130035827878542455979623747888891433345604817588712723282399687865427853871\ , 1460552582234841803
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Conjecture: a(n) is nonzero for all n>1. Generates surprisingly large primes that are easily certified using Elliptic curve techniques (Mathematica's NumberTheory`PrimeQ`). For n=24 no certifiable prime was found with fewer than 1024 digits. - Wouter Meeussen (wouter.meeussen(AT)pandora.be), Jun 04 2004
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EXAMPLE
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a(7) = 3 as 7^(1/7) =1.3204692477561... and the least prime is 3.
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MATHEMATICA
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<< NumberTheory`PrimeQ`; Table[{n, k = 1; While[temp = Floor[10^k FractionalPart[n^(1/n)]]; k < 256 && (temp === 1 || ! ProvablePrimeQ[temp]), k++ ]; temp, k}, {n, 2, 23}]
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CROSSREFS
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Cf. A095188.
Sequence in context: A114927 A087512 A125194 this_sequence A023932 A022074 A037938
Adjacent sequences: A095186 A095187 A095188 this_sequence A095190 A095191 A095192
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KEYWORD
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base,nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jun 02 2004
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EXTENSIONS
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Corrected and extended by Wouter Meeussen (wouter.meeussen(AT)pandora.be), Jun 04 2004
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