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%I #43 Sep 08 2022 08:46:14
%S 0,1,2,4,5,6,7,9,10,11,12,13,15,16,17,18,20,21,22,23,24,26,27,28,29,
%T 31,32,33,34,35,37,38,39,40,42,43,44,45,46,48,49,50,51,53,54,55,56,57,
%U 59,60,61,62,64,65,66,67,68,70,71,72,73,75,76,77,78,79,81,82,83,84
%N Nonnegative m for which 2*floor(m^2/11) = floor(2*m^2/11).
%C Also, nonnegative m not congruent to 3 or 8 (mod 11).
%C Integers x >= 0 satisfying k*floor(x^2/11) = floor(k*x^2/11) with k >= 0:
%C k = 0, 1: x = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ... (A001477);
%C k = 2: x = 0, 1, 2, 4, 5, 6, 7, 9, 10, 11, 12, 13, ... (this sequence);
%C k = 3: x = 0, 1, 5, 6, 10, 11, 12, 16, 17, 21, 22, ... (A265188);
%C k = 4..10: x = 0, 1, 10, 11, 12, 21, 22, 23, 32, 33, ... (A112654);
%C k > 10: x = 0, 11, 22, 33, 44, 55, 66, 77, 88, 99, ... (A008593).
%C Primes in sequence: 2, 5, 7, 11, 13, 17, 23, 29, 31, 37, 43, 53, 59, ...
%H Bruno Berselli, <a href="/A265187/b265187.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,1,-1).
%F G.f.: x^2*(1 + x + 2*x^2 + x^3 + x^4 + x^5 + 2*x^6 + x^7 + x^8)/((1 - x)^2*(1 + x + x^2)*(1 + x^3 + x^6)).
%F a(n) = a(n-1) + a(n-9) - a(n-10) for n>10.
%t Select[Range[0, 100], 2 Floor[#^2/11] == Floor[2 #^2/11] &]
%t Select[Range[0, 100], ! MemberQ[{3, 8}, Mod[#, 11]] &]
%t LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 1, -1}, {0, 1, 2, 4, 5, 6, 7, 9, 10, 11}, 80]
%o (Sage) [n for n in (0..100) if 2*floor(n^2/11) == floor(2*n^2/11)]
%o (Magma) [n: n in [0..100] | 2*Floor(n^2/11) eq Floor(2*n^2/11)];
%o (PARI) is(n)=2*(n^2\11) == (2*n^2)\11 \\ _Anders Hellström_, Dec 05 2015
%Y Cf. A008593, A112654, A265188.
%Y Cf. similar sequences provided by 2*floor(m^2/h) = floor(2*m^2/h): A005843 (h=2), A001477 (h=3,4), A008854 (h=5), A047266 (h=6), A047299 (h=7), A042965 (h=8), A060464 (h=9), A237415 (h=10), this sequence (h=11), A047263 (h=12).
%K nonn,easy
%O 1,3
%A _Bruno Berselli_, Dec 04 2015
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