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A280682 Integers m such that floor(sqrt(m)) is even. 1


%S 0,4,5,6,7,8,16,17,18,19,20,21,22,23,24,36,37,38,39,40,41,42,43,44,45,

%T 46,47,48,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,100,101,

%U 102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120

%N Integers m such that floor(sqrt(m)) is even.

%C Also integers m such that Sum_{k=1..m} floor(k/m) is even (cf. A006218). See the Mathematical Reflections link.

%C This sequence is composed of blocks of 1,5,9,13,... (A016813:4n+1) consecutive terms, separated by 3,7,11,15,... (A004767:4n+3) consecutive terms.

%H Michel Marcus, <a href="/A280682/b280682.txt">Table of n, a(n) for n = 1..4950</a>

%H Mathematical Reflections, <a href="https://www.awesomemath.org/wp-pdf-files/math-reflections/mr-2015-06/mr_5_2015_solutions_4.pdf">Solution to Problem O349</a>, Issue 6, 2015, p. 19.

%e 3 whose sqrt is 1.732... does not belong to this sequence.

%e 5 whose sqrt is 2.236... belongs to this sequence.

%o (PARI) isok(n) = (sqrtint(n) % 2) == 0; \\ _Michel Marcus_, Jan 07 2017

%Y Cf. A000196, A006218, A004767, A016813.

%K nonn,easy

%O 1,2

%A _Michel Marcus_, Jan 07 2017

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Last modified March 30 10:09 EDT 2020. Contains 333125 sequences. (Running on oeis4.)