A323356 For a rational number p/q let f(p/q) = (p+q) / (A000120(p) + A000120(q)); a(n) is obtained by iterating f, starting at n/1, until an integer is reached (and then a(n) = that integer), or if no integer is ever reached then a(n) = -1.

1, 2, 2, 2, 2, 2, 2, -1, 7, -1, 3, 7, 7, -1, 7, -1, 6, -1, 5, 7, 7, -1, -1, -1, -1, 8, -1, -1, 6, 8, -1, 8, 11, 8, 9, 8, -1, 8, 8, 11, -1, 11, 11, 11, -1, 11, 8, -1, 8, 11, -1, -1, 11, 11, 8, 16, -1, 15, 10, 16, -1, -1, 15, 14, 22, 14, 17, 23, 11, 15, 11, 11, 8, 12, 11, 11, 16, 12, 11

Offset

1,2

Links

Table of n, a(n) for n=1..79.

Example

13/1 -> 14/4=7/2 -> 9/4 -> 13/3 -> 16/5 -> 21/3 = 7 so a(13) = 7.
8/1 -> 9/2 -> 11/3 -> 14/5 -> 19/5 -> 24/5 -> 29/4 -> 33/5 -> 38/4=19/2 -> 21/4 -> 25/4 -> 29/4 and the 5-cycle repeats, so a(8) = -1.

Mathematica

Array[SelectFirst[Rest@ NestWhileList[(#1 + #2)/(DigitCount[#1, 2, 1] + DigitCount[#2, 2, 1]) & @@ {Numerator@ #, Denominator@ #} &, #, UnsameQ, All], IntegerQ] /. k_ /; MissingQ@ k -> -1 &, 79] (* Michael De Vlieger, Jan 18 2019 *)

Crossrefs

Cf. A000120, A058971, A059175, A323275, A323375.

Sequence in context: A194342 A230410 A044925 * A319244 A309286 A102671

Adjacent sequences: A323353 A323354 A323355 * A323357 A323358 A323359

Keyword

sign,base

Author

Ctibor O. Zizka, Jan 18 2019

Status

approved