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Rank of (4-r)*n when all the numbers (4-r)*j and (4+r)*k, where r = sqrt(2), j>=1, k>=1, are jointly ranked.
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%I #10 Sep 08 2022 08:46:19

%S 1,2,4,5,7,8,10,11,13,14,16,17,19,20,22,23,25,26,28,29,31,32,33,35,36,

%T 38,39,41,42,44,45,47,48,50,51,53,54,56,57,59,60,62,63,65,66,67,69,70,

%U 72,73,75,76,78,79,81,82,84,85,87,88,90,91,93,94,96,97

%N Rank of (4-r)*n when all the numbers (4-r)*j and (4+r)*k, where r = sqrt(2), j>=1, k>=1, are jointly ranked.

%H Clark Kimberling, <a href="/A292640/b292640.txt">Table of n, a(n) for n = 1..1000</a>

%t z = 120; r = 4 - Sqrt[2]; s = 4 + Sqrt[2];

%t Table[n + Floor[n*r/s], {n, 1, z}] (* A292640 *)

%t Table[n + Floor[n*s/r], {n, 1, z}] (* A292641 *)

%o (PARI) vector(100, n, n+floor(n*(4-sqrt(2))/(4+sqrt(2)))) \\ _G. C. Greubel_, Aug 20 2018

%o (Magma) [n+Floor(n*(4-Sqrt(2))/(4+Sqrt(2))): n in [1..100]]; // _G. C. Greubel_, Aug 20 2018

%Y Cf. A292641 (complement).

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Sep 26 2017