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A066494
Numbers n such that prime(n+1) - prime(n) = phi(n).
0
1, 3, 8, 9, 12, 18, 24
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
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
KEYWORD
more,nonn,fini
AUTHOR
Joseph L. Pe, Jan 03 2002
STATUS
approved