A371702 - OEIS

%I #8 Apr 04 2024 10:27:27

%S 1,1,1,3,5,8,12,16,21,26,32,39,46,54,63,72,82,92,103,115,128,141,154,

%T 169,184,199,215,232,250,268,287,306,326,347,368,390,413,436,460,484,

%U 510,535,562,589,616,645,674,703,734,765,796,828,861,894,928,963

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

%F a(n) ~ n^2 / Pi. - _Vaclav Kotesovec_, Apr 03 2024

%e a(4) = 5: (2/1) * (4/3) * (6/5) * (8/7) * (10/9) = 256 / 63 = 4.063492... > 4.

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

%o (PARI) a(n) = my(k=1); while (prod(i=1, k, 1 + 1/(2*i-1)) < n, k++); k; \\ _Michel Marcus_, Apr 03 2024

%Y Cf. A000165, A001147, A001803, A046161, A072986, A371701.

%K nonn

%O 0,4

%A _Ilya Gutkovskiy_, Apr 03 2024