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Search: id:A066494
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| A066494 |
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Numbers n such that p(n+1)-p(n) = EulerPhi(n), where p(n) denotes the n-th prime. |
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OFFSET
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1,2
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COMMENT
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After 24, there are no more terms < 10^6. Are there any more terms?
This sequence is certainly finite and very likely complete. phi(n) is bounded below asymptotically by n/log log n * e^{-gamma}, while prime gaps are known to be bounded asymptotically above by p^{1/3} ~ (n log n)^(1/3). - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jul 27 2006
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EXAMPLE
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p(13)-p(12) = 41 - 37 = 4 = EulerPhi(12); so 12 belongs to the sequence.
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MATHEMATICA
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f[n_] := Prime[n + 1] - Prime[n]; Select[Range[1, 10^6], f[ # ] == EulerPhi[ # ] &]
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CROSSREFS
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Adjacent sequences: A066491 A066492 A066493 this_sequence A066495 A066496 A066497
Sequence in context: A080761 A087286 A165289 this_sequence A082721 A071677 A084747
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KEYWORD
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more,nonn,fini
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AUTHOR
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Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Jan 03 2002
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