A179272 -id:A179272 - cp's OEIS frontend

A179273 Primes in A179272.

2, 5, 7, 11, 19, 23, 29, 41, 47, 71, 79, 89, 109, 131, 167, 181, 223, 239, 271, 359, 379, 419, 439, 461, 599, 701, 727, 811, 839, 929, 991, 1087, 1223, 1259, 1367, 1481, 1559, 1721, 1847, 1979, 2069, 2161, 2207, 2351, 2399, 2549, 2861, 2969, 3023, 3079, 3191

Offset: 1

Jonathan Vos Post, Jul 07 2010

Primes of form floor(((n^2)/4) - (n/2) - 1). Primes in sharp upper bound on Rosgen overlap number n-vertex graph with n => 14, formula abused here for nonnegative integers. There seem to be more primes (29) through n = 60 of floor(((n^2)/4) - (n/2) - 1) than one might expect. What fraction through n = 1000 are prime?

			a(1) = floor(((5^2)/4) - (5/2) - 1) = floor(16/4 - 5/2 - 1) = floor(11/4) = 2.
a(2) = floor(((6^2)/4) - (6/2) - 1) = floor(36/4 - 6/2 - 1) = floor(5) = 5.

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Daniel W. Cranston, Nitish Korula, Timothy D. LeSaulnier, Kevin Milans, Christopher Stocker, Jennifer Vandenbussche, Douglas B. West, Overlap Number of Graphs, Jul 06, 2010.

Cf. A000040, A179272.

Select[Table[Floor[n^2/4-n/2-1],{n,5,200}],PrimeQ] (* Harvey P. Dale, Oct 12 2012 *)

More terms from R. J. Mathar, Oct 15 2010

A183867 a(n) = n + floor(2*sqrt(n)); complement of A184676.

Original entry on oeis.org

3, 4, 6, 8, 9, 10, 12, 13, 15, 16, 17, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 31, 32, 33, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 80, 81, 82, 83

Offset: 1

Clark Kimberling, Jan 07 2011

Also equals n + floor(sqrt(n) + sqrt(n+1/2)). Proof: floor(2*sqrt(n)) is the largest k such that k^2/4 <= n, while floor(sqrt(n) + sqrt(n+1/2)) is the largest k such that (k^2 - 1)/4 + 1/(16*k^2) <= n. All perfect squares are 0 or 1 (mod 4). In either case, it is easily verified that one of the inequalities is satisfied if and only if the other inequality is satisfied. - Nathaniel Johnston, Jun 26 2011

Nathaniel Johnston, Table of n, a(n) for n = 1..5000

Cf. A179272.

[n+Floor(2*Sqrt(n)): n in [1..100]]; // Vincenzo Librandi, Dec 09 2015

seq(n+floor(2*sqrt(n)), n=1..67); # Nathaniel Johnston, Jun 26 2011

a=4; b=0;
Table[n+Floor[(a*n+b)^(1/2)],{n,100}]
Table[n-1+Ceiling[(n*n-b)/a],{n,70}]

a(n) =  n+sqrtint(4*n); \\ Michel Marcus, Dec 08 2015, Jul 28 2025

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A179273 Primes in A179272.

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