|
Search: id:A066494
|
|
|
| A066494 |
|
Numbers n such that p(n+1)-p(n) = EulerPhi(n), where p(n) denotes the n-th prime. |
|
+0
1
|
| |
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
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
|
|
EXAMPLE
|
p(13)-p(12) = 41 - 37 = 4 = EulerPhi(12); so 12 belongs to the sequence.
|
|
MATHEMATICA
|
f[n_] := Prime[n + 1] - Prime[n]; Select[Range[1, 10^6], f[ # ] == EulerPhi[ # ] &]
|
|
CROSSREFS
|
Sequence in context: A080761 A087286 A165289 this_sequence A082721 A071677 A084747
Adjacent sequences: A066491 A066492 A066493 this_sequence A066495 A066496 A066497
|
|
KEYWORD
|
more,nonn,fini
|
|
AUTHOR
|
Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Jan 03 2002
|
|
|
Search completed in 0.002 seconds
|
