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Search: id:A072923
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| A072923 |
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Number of primes of the form floor( (1+1/k)^n ) 1<=k<=n. |
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+0
1
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| 1, 1, 2, 3, 3, 5, 5, 4, 6, 5, 8, 5, 7, 6, 7, 7, 10, 8, 9, 8, 11, 12, 10, 12, 14, 10, 15, 13, 13, 17, 16, 16, 17, 14, 18, 18, 17, 22, 18, 22, 16, 21, 23, 20, 20, 24, 22, 24, 26, 23, 23, 26, 25, 26, 25, 28, 25, 31, 29, 26, 31, 27, 28, 31, 32, 31, 37, 32, 29, 32, 34, 31, 35, 34, 32
(list; graph; listen)
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OFFSET
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1,3
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FORMULA
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Conjecture: a(n) is asymptotic to C*n with C = 0.47......
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EXAMPLE
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floor((1+1/k)^15 is prime for k = 7,8,11,12,13,14,15 (giving the successive prime values 7,5,3,3,3,2,2) hence a(15)=7
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PROGRAM
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(PARI) a(n)=if(n<0, 0, sum(k=1, n, if(isprime(floor((1+1/k)^n)), 1, 0)))
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CROSSREFS
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Sequence in context: A103310 A046146 A081768 this_sequence A131922 A113730 A154404
Adjacent sequences: A072920 A072921 A072922 this_sequence A072924 A072925 A072926
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KEYWORD
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easy,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 11 2002
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