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%I #8 Nov 17 2021 17:12:09
%S 1,0,0,0,0,0,1,0,0,0,1,0,0,0,1,1,0,0,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0,
%T 0,0,1,1,0,0,0,0,1,1,0,0,1,0,0,0,1,1,1,0,0,0,0,1,1,0,0,0,1,1,1,0,0,1,
%U 0,0,0,1,1,0,0,0,1,1,0,0,1,0,0,0,1,1,1,0,0,0,0,0,0,0,1
%N Parity of A347113.
%C Terms k = A347113(n) conspicuously greater than n are even, though most even k are less than n. Given 2^19 terms of A347113, 45620 even terms exceed n, while 237855 are less than n, and 19 fixed points are even. Odd k are largely less than n; for 2^19 terms of A347113, there are 12 odd terms that exceed n, e.g., A347113(85) = 87, and 1 odd fixed point A347113(1) = 1. - _Michael De Vlieger_, Nov 16 2021
%H Michael De Vlieger, <a href="/A347312/b347312.txt">Table of n, a(n) for n = 1..10000</a>
%H Michael De Vlieger, <a href="/A347312/a347312.png">Log-log scatterplot of A347113(n)</a>, n=1..2^19, indicating parity, even terms in blue, odds in red.
%t c[_] = 0; j = m = 2; {1}~Join~Reap[Do[If[IntegerQ@ Log2[i], While[c[m] > 0, m++]]; Set[k, m]; While[Or[c[k] > 0, k == j, GCD[j, k] == 1], k++]; Sow[Boole@ OddQ@ k]; Set[c[k], i]; j = k + 1, {i, 105}]][[-1, -1]] (* _Michael De Vlieger_, Nov 16 2021 *)
%Y Cf. A347113.
%K nonn
%O 1
%A _N. J. A. Sloane_, Sep 06 2021
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