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 A066494 Numbers n such that prime(n+1) - prime(n) = phi(n). 0
 1, 3, 8, 9, 12, 18, 24 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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). - Franklin T. Adams-Watters, Jul 27 2006 LINKS Table of n, a(n) for n=1..7. EXAMPLE Prime(13) - prime(12) = 41 - 37 = 4 = phi(12), so 12 belongs to the sequence. MATHEMATICA f[n_] := Prime[n + 1] - Prime[n]; Select[Range[1, 10^6], f[ # ] == EulerPhi[ # ] &] PrimePi[#]&/@Select[Partition[Prime[Range[25]], 2, 1], #[[2]]-#[[1]]==EulerPhi[ PrimePi[ #[[1]]]]&][[All, 1]] (* Harvey P. Dale, Sep 09 2022 *) CROSSREFS Sequence in context: A080761 A087286 A165289 * A082721 A239388 A259850 Adjacent sequences: A066491 A066492 A066493 * A066495 A066496 A066497 KEYWORD more,nonn,fini AUTHOR Joseph L. Pe, Jan 03 2002 STATUS approved

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Last modified December 9 01:07 EST 2023. Contains 367681 sequences. (Running on oeis4.)