A066494 Numbers n such that prime(n+1) - prime(n) = phi(n).

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

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