login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A309945 a(n) = floor(n - sqrt(2*n-1)). 1
0, 0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 7, 8, 8, 9, 10, 11, 12, 12, 13, 14, 15, 16, 17, 18, 18, 19, 20, 21, 22, 23, 24, 24, 25, 26, 27, 28, 29, 30, 31, 32, 32, 33, 34, 35, 36, 37, 38, 39, 40, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 60 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

The subsequence consisting of numbers that appear twice is A007590.

Sequence as triangle:

   0;

   0;

   0;  1,  2;

   2,  3,  4;

   4,  5,  6,  7,  8;

   8,  9, 10, 11, 12;

  12, 13, 14, 15, 16, 17, 18;

  18, 19, 20, 21, 22, 23, 24;

  ...

a(1) = 0; for n > 1, a(n) is the number of squares strictly between 2*n - 2 and n^2.

LINKS

Table of n, a(n) for n = 1..999

FORMULA

a(n) = n-1-floor(sqrt(2*n-2)). - Wesley Ivan Hurt, Dec 03 2020

EXAMPLE

For n = 3, 2*n - 2 = 4, n^2 = 9, no square numbers strictly between 4 and 9, a(3) = 0.

For n=5, 2*n - 2 = 8, n^2 = 25, two square numbers (9, 16) strictly between 8 and 25, a(5) = 2.

MATHEMATICA

Table[Floor[n-(2*n-1)^(1/2)], {n, 73}] (* Stefano Spezia, Aug 24 2019 *)

PROG

(PARI) a(n) = floor(n - sqrt(2*n-1)); \\ Jinyuan Wang, Aug 26 2019

CROSSREFS

Cf. A007590, A080476, A016813.

Sequence in context: A122797 A281957 A286389 * A103354 A127038 A175268

Adjacent sequences:  A309942 A309943 A309944 * A309946 A309947 A309948

KEYWORD

nonn

AUTHOR

Zhandos Mambetaliyev, Aug 24 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 18 06:58 EDT 2021. Contains 345098 sequences. (Running on oeis4.)