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Rank of (6-r)*n when all the numbers (6-r)*j and (6+r)*k, where r = sqrt(2), j>=1, k>=1, are jointly ranked.
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%I #13 Aug 28 2022 08:37:02

%S 1,3,4,6,8,9,11,12,14,16,17,19,21,22,24,25,27,29,30,32,33,35,37,38,40,

%T 42,43,45,46,48,50,51,53,55,56,58,59,61,63,64,66,67,69,71,72,74,76,77,

%U 79,80,82,84,85,87,89,90,92,93,95,97,98,100,101,103,105

%N Rank of (6-r)*n when all the numbers (6-r)*j and (6+r)*k, where r = sqrt(2), j>=1, k>=1, are jointly ranked.

%C First differs from A000201 at a(55) = 89 <> 88. - _Peter Munn_, Aug 27 2022

%H Clark Kimberling, <a href="/A292644/b292644.txt">Table of n, a(n) for n = 1..1000</a>

%t z = 120; r = 6 - Sqrt[2]; s = 6 + Sqrt[2];

%t Table[n + Floor[n*r/s], {n, 1, z}] (* A292644 *)

%t Table[n + Floor[n*s/r], {n, 1, z}] (* A292645 *)

%o (PARI) vector(100, n, n+floor(n*(6-sqrt(2))/(6+sqrt(2)))) \\ _G. C. Greubel_, Aug 20 2018

%o (Magma) [n+Floor(n*(6-Sqrt(2))/(6+Sqrt(2))): n in [1..100]]; // _G. C. Greubel_, Aug 20 2018

%Y Cf. A000201, A292645 (complement).

%Y Equivalent sequences with 6 replaced in the definition by m: A292636 (m=3), A292640 (m=4), A292642 (m=5).

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Sep 26 2017