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

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, 46, 47, 48, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120

Offset

1,2

Comments

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

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.

Links

Michel Marcus, Table of n, a(n) for n = 1..4950

Mathematical Reflections, Solution to Problem O349, Issue 6, 2015, p. 19.

Example

3 whose sqrt is 1.732... does not belong to this sequence.
5 whose sqrt is 2.236... belongs to this sequence.

Mathematica

Select[Range[0, 150], EvenQ[Floor[Sqrt[#]]]&] (* Harvey P. Dale, Jun 06 2024 *)

Prog

(PARI) isok(n) = (sqrtint(n) % 2) == 0; \\ Michel Marcus, Jan 07 2017

Crossrefs

Cf. A000196, A006218, A004767, A016813.

Sequence in context: A344580 A071623 A274552 * A140293 A075341 A309358

Adjacent sequences: A280679 A280680 A280681 * A280683 A280684 A280685

Keyword

nonn,easy

Author

Michel Marcus, Jan 07 2017

Status

approved