A291271 The arithmetic function v_4(n,2).

0, 1, 0, 2, 2, 3, 2, 4, 4, 5, 4, 6, 6, 7, 6, 8, 8, 9, 8, 10, 10, 11, 10, 12, 12, 13, 12, 14, 14, 15, 14, 16, 16, 17, 16, 18, 18, 19, 18, 20, 20, 21, 20, 22, 22, 23, 22, 24, 24, 25, 24, 26, 26, 27, 26, 28, 28, 29, 28, 30, 30, 31, 30, 32, 32, 33, 32, 34, 34

Offset

2,4

Comments

For any integer n>=7, a(n) is the smallest number of diametrical slices needed to divide two pizzas equally between n-4 people. - Jamil Silva, Mar 29 2025

References

J. Butterworth, Examining the arithmetic function v_g(n,h). Research Papers in Mathematics, B. Bajnok, ed., Gettysburg College, Vol. 8 (2008).

Links

Table of n, a(n) for n=2..70.

Bela Bajnok, Additive Combinatorics: A Menu of Research Problems, arXiv:1705.07444 [math.NT], May 2017. See Table in Section 1.6.1.

Formula

Conjecture: a(n) = (n-2-cos(n*Pi)-cos(n*Pi/2))/2. - Wesley Ivan Hurt, Oct 02 2017

a(n) = (n-gcd(n,4))/2 = A291330(n)/2. - Ridouane Oudra, Dec 28 2024

Sum_{n>=5} (-1)^n/a(n) = 1 - log(2) (A244009). - Amiram Eldar, Jan 15 2025

a(2)=a(4)=0, a(3)=1, a(5)=a(6)=2, a(2n+5)=n+2, a(4n+4)=2n, a(4n+6)=2n+2. - Jamil Silva, Mar 29 2025

Maple

seq((n-gcd(n, 4))/2, n=2..80); # Ridouane Oudra, Dec 28 2024

Mathematica

v[g_, n_, h_] := (d = Divisors[n]; Max[(Floor[(d - 1 - GCD[d, g])/h] + 1)*n/d]); Table[v[4, n, 2], {n, 2, 70}]

Crossrefs

Cf. A244009, A289435, A289436, A289437, A289438, A289439, A289440, A289441.

Cf. A291330.

Sequence in context: A307797 A233777 A048620 * A308318 A165419 A117660

Adjacent sequences: A291268 A291269 A291270 * A291272 A291273 A291274

Keyword

nonn

Author

Robert Price, Aug 21 2017

Status

approved