

A066494


Numbers n such that prime(n+1)  prime(n) = phi(n).


0




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. AdamsWatters, Jul 27 2006


LINKS



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



KEYWORD

more,nonn,fini


AUTHOR



STATUS

approved



