

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



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
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OFFSET

1,2


LINKS



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 5cycle 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



KEYWORD

sign,base


AUTHOR



STATUS

approved



