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%I #34 Jan 19 2019 03:50:13
%S 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,
%T 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,
%U 16,-1,15,10,16,-1,-1,15,14,22,14,17,23,11,15,11,11,8,12,11,11,16,12,11
%N 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.
%e 13/1 -> 14/4=7/2 -> 9/4 -> 13/3 -> 16/5 -> 21/3 = 7 so a(13) = 7.
%e 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.
%t 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 *)
%Y Cf. A000120, A058971, A059175, A323275, A323375.
%K sign,base
%O 1,2
%A _Ctibor O. Zizka_, Jan 18 2019
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