A371701 a(n) is the least positive k such that Product_{i=1..k} 1 / (1 - 1/(2*i+1)) >= n.

1, 1, 3, 7, 12, 19, 28, 38, 50, 63, 78, 95, 113, 132, 154, 176, 201, 227, 254, 283, 314, 346, 380, 415, 452, 491, 531, 572, 616, 660, 707, 755, 804, 855, 908, 962, 1018, 1075, 1134, 1194, 1256, 1320, 1385, 1452, 1520, 1590, 1662, 1735, 1809, 1885, 1963, 2043, 2123, 2206, 2290, 2376

Offset

0,3

Links

Table of n, a(n) for n=0..55.

Formula

a(n) ~ Pi * n^2 /4. - Vaclav Kotesovec, Apr 03 2024

Example

a(3) = 7: (3/2) * (5/4) * (7/6) * (9/8) * (11/10) * (13/12) * (15/14) = 6435 / 2048 = 3.14208984375 > 3.

Mathematica

a[n_] := For[k = 1, True, k++, If[(2 k + 1)!!/(2 k)!! >= n, Return[k]]]; Table[a[n], {n, 0, 55}]

Crossrefs

Cf. A000165, A001147, A001803, A005579, A046161, A256968, A371702.

Sequence in context: A022330 A303279 A024219 * A283733 A025713 A022791

Adjacent sequences: A371698 A371699 A371700 * A371702 A371703 A371704

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 03 2024

Status

approved