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Search: id:A083684
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| A083684 |
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n-th natural number such that there isn't exist nonnegative integer m, m < n *prime(n) which fp(n,m)=prime(1)m prime(2)m...prime(n-1)m prime(n) is prime. |
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+0
2
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| 1, 3, 10, 16, 28, 34, 40, 46, 52, 70, 76, 82, 88, 97, 103, 121, 127, 136, 163, 166, 169, 175, 187, 199, 205, 211, 217, 220, 235, 250, 262, 268
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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I found a(n) for n <=32. I conjecture that a(1)=1,a(2)=3 and a(n+2) is n-th nutural number such that g(n)=prime(1)+prime(2)+...+prime(n)=n-1=0 ( mod 3). ( fp(1,m) isn't defined fp(3,m)=0 (mod 5) and if g(n)=n-1=0 ( mod 3) sum of digits of fp(n,m)=(n-1)m+g(n)=0 ( mod 3) thus fp(n,m) isn't prime).
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EXAMPLE
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a(3)=10 because fp(2,2),fp(4,1),fp(5,4),fp(6,10),fp(7,38),fp(8,20),fp(9,0) are prime numbers and fp(1,m) isn't defined fp(3,m)=0( mod 5) and fp(10,m)=0 ( mod 3) for each m.
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CROSSREFS
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Cf. A082549.
Sequence in context: A093516 A063209 A063109 this_sequence A059911 A043405 A063293
Adjacent sequences: A083681 A083682 A083683 this_sequence A083685 A083686 A083687
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KEYWORD
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nonn,uned
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AUTHOR
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Farideh Firoozbakht (f.firoozbakht(AT)sci.ui.ac.ir), Jun 15 2003
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