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Search: id:A085918
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| A085918 |
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Primes p such that for some k the number of terms > 0 and < 1 in the Farey sequence of order k is p. |
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+0
1
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| 3, 5, 11, 17, 31, 41, 71, 79, 101, 127, 139, 149, 179, 199, 211, 229, 241, 269, 277, 307, 359, 383, 431, 449, 541, 773, 829, 881, 1259, 1307, 1327, 1493, 1831, 1933, 2141, 2551, 3373, 3947, 4127, 4831, 4957, 5021, 5153, 5323, 5431, 5569, 5813, 6091, 6329
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Or, prime numbers of the form Sum(phi(j), j=2..n). - Jorge Coveiro (jorgecoveiro(AT)yahoo.com), Dec 22 2004. Examples: phi(2)+phi(3)= 3; phi(2)+phi(3)+phi(4)= 5; phi(2)+phi(3)+phi(4)+phi(5)+phi(6)= 11; phi(2)+phi(3)+phi(4)+phi(5)+phi(6)+phi(7)= 17.
Does this sequence have an infinite number of terms?
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EXAMPLE
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The Farey sequence of order 4 is {0, 1/4, 1/3, 1/2, 2/3, 3/4, 1}. The number of terms > 0 and < 1 is 5, which is prime, so 5 is a member.
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PROGRAM
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(PARI) \ Farey sequence of order n fareycountp(n) = { for(x=2, n, y = farey(x); if(isprime(y), print1(y", ")); ) } farey(n) = { c=1; m=n*(n-2)+2; a=vector(m); for(x=1, n, for(y=x, n, v = x/y; if(v<1, c++; a[c]=v; ) ) ); a = vecsort(a); c=0; for(x=2, m, if(a[x]<>a[x-1] & a[x]<>0, \ print1(a[x]", "); c++; ) ); return(c) }
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CROSSREFS
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Cf. A078334, A005728, A101300, A000010.
Sequence in context: A087732 A108542 A006450 this_sequence A146622 A124179 A124173
Adjacent sequences: A085915 A085916 A085917 this_sequence A085919 A085920 A085921
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KEYWORD
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easy,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Aug 16 2003
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EXTENSIONS
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Definition corrected by Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Apr 21 2005
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