A347312 Parity of A347113.

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, 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, 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

Offset

1

Comments

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

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Michael De Vlieger, Log-log scatterplot of A347113(n), n=1..2^19, indicating parity, even terms in blue, odds in red.

Mathematica

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 *)

Crossrefs

Cf. A347113.

Sequence in context: A319691 A079979 A288711 * A089010 A162289 A373139

Adjacent sequences: A347309 A347310 A347311 * A347313 A347314 A347315

Keyword

nonn

Author

N. J. A. Sloane, Sep 06 2021

Status

approved