A332971 Infinitary phibonacci numbers: solutions k of the equation iphi(k) = iphi(k-1) + iphi(k-2) where iphi(k) is an infinitary analog of Euler's phi function (A091732).

3, 4, 7, 23, 121, 2857, 5699, 6377, 9179, 46537, 63209, 244967, 654497, 1067873, 1112009, 3435929, 3831257, 6441593, 7589737, 7784507, 8149751, 14307856, 22434089, 24007727, 24571871, 44503417, 44926463, 56732729, 128199059, 140830367, 190145936, 401767631, 403152737

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..70

Example

7 is a term since iphi(7) = 6 and iphi(5) + iphi(6) = 4 + 2 = 6.

Mathematica

f[p_, e_] := p^(2^(-1 + Position[Reverse@IntegerDigits[e, 2], 1])); iphi[1] = 1; iphi[n_] := Times @@ (Flatten @ (f @@@ FactorInteger[n]) - 1); Select[Range[3, 10^5], iphi[#] == iphi[# - 1] + iphi[# - 2] &]

Crossrefs

An infinitary version of A065557.

Cf. A065900, A075565, A076136, A076251, A091732, A145469, A291126, A291176, A292033, A294995.

Sequence in context: A056655 A341810 A338511 * A292033 A288501 A288019

Adjacent sequences: A332968 A332969 A332970 * A332972 A332973 A332974

Keyword

nonn

Author

Amiram Eldar, Mar 04 2020

Status

approved