A371702 a(n) is the least positive k such that Product_{i=1..k} (1 + 1/(2*i-1)) >= n.
1, 1, 1, 3, 5, 8, 12, 16, 21, 26, 32, 39, 46, 54, 63, 72, 82, 92, 103, 115, 128, 141, 154, 169, 184, 199, 215, 232, 250, 268, 287, 306, 326, 347, 368, 390, 413, 436, 460, 484, 510, 535, 562, 589, 616, 645, 674, 703, 734, 765, 796, 828, 861, 894, 928, 963
Offset: 0
Keywords
Examples
a(4) = 5: (2/1) * (4/3) * (6/5) * (8/7) * (10/9) = 256 / 63 = 4.063492... > 4.
Programs
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Mathematica
a[n_] := For[k = 1, True, k++, If[(2 k)!!/(2 k - 1)!! >= n, Return[k]]]; Table[a[n], {n, 0, 55}] -
PARI
a(n) = my(k=1); while (prod(i=1, k, 1 + 1/(2*i-1)) < n, k++); k; \\ Michel Marcus, Apr 03 2024
Formula
a(n) ~ n^2 / Pi. - Vaclav Kotesovec, Apr 03 2024