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Search: id:A098006
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| A098006 |
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(p-1)/2 - phi(p-1) as p runs through the odd primes. |
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+0
6
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| 0, 0, 1, 1, 2, 0, 3, 1, 2, 7, 6, 4, 9, 1, 2, 1, 14, 13, 11, 12, 15, 1, 4, 16, 10, 19, 1, 18, 8, 27, 17, 4, 25, 2, 35, 30, 27, 1, 2, 1, 42, 23, 32, 14, 39, 57, 39, 1, 42, 4, 23, 56, 25, 0, 1, 2, 63, 50, 44, 49, 2, 57, 35, 60, 2, 85, 72, 1, 62, 16, 1, 63, 66, 81, 1, 2, 78, 40, 76, 29, 114, 47
(list; graph; listen)
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OFFSET
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2,5
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COMMENT
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In the Luca-Walsh paper it is shown that there are infinitely many numbers not in this sequence. See A098047.
a(n)=0 for Fermat primes (A019434). a(n)=1 for safe primes (A005385). a(n)=2 for A090866. The least prime p for which (p-1)/2-phi(p-1)=n or 0 if there is no such prime is given by A134765(n). Sequence A134854(k) gives the least prime for which a(n)=2^(k-1). For k not a power of 2, it can be shown that if k is in this sequence, then it appears for a prime p <= 1+k^2. - T. D. Noe, Nov 13 2007
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REFERENCES
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J. Browkin and A. Schinzel, On integers not of the form n-phi(n), Colloq. Math., 68 (1995), 55-58.
F. Luca and P. G. Walsh, On the number of nonquadratic residues which are not primitive roots, Colloq. Math., 100 (2004), 91-93.
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LINKS
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T. D. Noe, Table of n, a(n) for n=2..10000
T. D. Noe, Finding primes p for which (p-1)/2 - phi(p-1) = k
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MATHEMATICA
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Table[(Prime[n] - 1)/2 - EulerPhi[Prime[n] - 1], {n, 2, 85}] (from Robert G. Wilson v Sep 09 2004)
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CROSSREFS
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Cf. A000010, A051953, A098047.
Sequence in context: A071504 A125943 A167565 this_sequence A082650 A015710 A054875
Adjacent sequences: A098003 A098004 A098005 this_sequence A098007 A098008 A098009
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Sep 08 2004
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