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A265188 Nonnegative m for which 3*floor(m^2/11) = floor(3*m^2/11). 3

%I

%S 0,1,5,6,10,11,12,16,17,21,22,23,27,28,32,33,34,38,39,43,44,45,49,50,

%T 54,55,56,60,61,65,66,67,71,72,76,77,78,82,83,87,88,89,93,94,98,99,

%U 100,104,105,109,110,111,115,116,120,121,122,126,127,131,132,133,137,138,142

%N Nonnegative m for which 3*floor(m^2/11) = floor(3*m^2/11).

%C See the second comment in A265187.

%C Also, nonnegative m congruent to 0, 1, 5, 6 or 10 (mod 11).

%C Primes in sequence: 5, 11, 17, 23, 43, 61, 67, 71, 83, 89, 109, 127, ...

%H Bruno Berselli, <a href="/A265188/b265188.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1).

%F G.f.: x^2*(1 + 4*x + x^2 + 4*x^3 + x^4)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4)).

%F a(n) = a(n-1) + a(n-5) - a(n-6), n>6.

%t Select[Range[0, 150], 3 Floor[#^2/11] == Floor[3 #^2/11] &]

%t Select[Range[0, 150], MemberQ[{0, 1, 5, 6, 10}, Mod[#, 11]] &]

%t LinearRecurrence[{1, 0, 0, 0, 1, -1}, {0, 1, 5, 6, 10, 11}, 70]

%o (Sage) [n for n in (0..150) if 3*floor(n^2/11) == floor(3*n^2/11)]

%o (MAGMA) [n: n in [0..150] | 3*Floor(n^2/11) eq Floor(3*n^2/11)];

%o (PARI) is(n) = 3*(n^2\11) == (3*n^2)\11 \\ _Anders Hellström_, Dec 05 2015

%o (PARI) concat(0, Vec(x^2*(1 + 4*x + x^2 + 4*x^3 + x^4)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4)) + O(x^100))) \\ _Michel Marcus_, Dec 05 2015

%Y Cf. A265187.

%Y Cf. similar sequences provided by 3*floor(n^2/h) = floor(3*n^2/h): A005843 (h=2), A008585 (h=3), A001477 (h=4), A008854 (h=5), A047266 (h=6), A047299 (h=7), A042965 (h=8), A265227 (h=9), A054967 (h=10), this sequence (h=11), A047266 (h=12).

%K nonn,easy

%O 1,3

%A _Bruno Berselli_, Dec 04 2015

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Last modified July 23 22:20 EDT 2021. Contains 346265 sequences. (Running on oeis4.)