A070959 First minimum value > 0 of the form x^3-k^2 when k > n^3.

4, 4, 39, 13, 152, 28, 391, 49, 804, 76, 1439, 109, 2344, 148, 3567, 193, 5156, 244, 7159, 301, 9624, 364, 12599, 433, 16132, 508, 20271, 589, 25064, 676, 30559, 769, 36804, 868, 43847, 973, 51736, 1084, 60519, 1201, 70244, 1324, 80959, 1453, 92712

Offset: 1

Author

Benoit Cloitre, May 25 2002

Keywords

• easy
• nonn

Examples

			Let n=2 then n^3=8 and A070923(9)= 44, A070923(10)=25, A070923(11)=4, A070923(12)=72 so the first minimum is 4, hence a(2)=4
		

Crossrefs

Cf. A070923.

Programs

PARI

for(n=1,100,s=n^3+1; while(ceil(s^(2/3))^3-s^2>ceil((s+1)^(2/3))^3-(s+1)^2,s++); print1(ceil(s^(2/3))^3-s^2,","))

Formula

Let k be the smallest integer>n^3 such that A070923(k-1)> A070923(k) and such that A070923(k) < A070923(k+1), then a(n)= A070923(k); for n>=1 a(2n-1) = 8n^3-9n^2+6n-1, a(2n)=3n^2+1.

From Chai Wah Wu, Jul 27 2020: (Start)

a(n) = 4*a(n-2) - 6*a(n-4) + 4*a(n-6) - a(n-8) for n > 8.

G.f.: x*(-x^7 + x^6 + 20*x^4 - 3*x^3 + 23*x^2 + 4*x + 4)/((x - 1)^4*(x + 1)^4). (End)