A117290 Numbers k for which the cototient k - phi(k) is a Fibonacci number.

1, 2, 3, 4, 5, 7, 9, 11, 12, 13, 14, 16, 17, 19, 23, 25, 29, 31, 33, 37, 41, 43, 45, 47, 53, 57, 59, 61, 67, 71, 73, 79, 83, 85, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 159, 163, 167, 169, 173, 175, 179, 181, 191, 193, 197, 199, 211, 216, 223

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

33 is in the sequence because 33 - phi(33) = 13, which is a Fibonacci number.

Mathematica

With[{fibs=Fibonacci[Range[0, 13]]}, Select[Range[fibs[[-1]]], MemberQ[fibs, #-EulerPhi[#]]&]] (* Harvey P. Dale, Jan 28 2011 *)

Prog

(PARI) isfib(n) = my(k=n^2); k+=(k+1)<<2; issquare(k) || (n>0 && issquare(k-8));
isok(n) = isfib(n-eulerphi(n)); \\ Michel Marcus, Mar 23 2021

Crossrefs

Cf. A000010, A000045, A051953.

Sequence in context: A178434 A267439 A262691 * A286972 A210994 A331593

Adjacent sequences: A117287 A117288 A117289 * A117291 A117292 A117293

Keyword

nonn

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 23 2006

Extensions

Offset corrected and a(1) added by Amiram Eldar, Mar 23 2021

Status

approved