A114458 Integer part of sqrt(n)+sqrt(n+1)+sqrt(n+2).

4, 5, 5, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 11, 12, 12, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 20, 21, 21, 21, 21, 22, 22, 22, 22, 22, 23, 23, 23, 23, 23, 23, 24, 24, 24, 24, 24, 25, 25, 25, 25, 25

Offset

1,1

References

Prapanpong Pongsriiam, Analytic Number Theory for Beginners, 2nd edition, American Mathematical Society, 2023.

Links

Table of n, a(n) for n=1..73.

John D. Cook, Floors and roots.

F. D. Hammer, Problem E3010, Amer. Math. Monthly, 95, 1988, 133-134.

X. Zhan, Formulae for sums of consecutive square roots, The Math. Intelligencer, 27, No. 4, 2005, 4-5.

Formula

a(n) = floor(sqrt(9n+8)).

Maple

seq(floor(sqrt(9*n+8)), n=1..90);

Mathematica

IntegerPart/@(Total/@Partition[Sqrt[Range[80]], 3, 1]) (* Harvey P. Dale, May 03 2013 *)

Prog

(PARI) vector(80, n, sqrtint(9*n+8)) \\ Michel Marcus, Jun 27 2015
(Magma) [Floor(Sqrt(9*n+8)): n in [1..70]]; // Vincenzo Librandi, Jun 28 2015

Crossrefs

Cf. A000267, A114459, A114460.

Sequence in context: A350361 A205677 A178400 * A205842 A061508 A120189

Adjacent sequences: A114455 A114456 A114457 * A114459 A114460 A114461

Keyword

nonn

Author

Emeric Deutsch, Nov 28 2005

Status

approved