A371701 - OEIS

%I #9 Jan 25 2025 15:28:58

%S 1,1,3,7,12,19,28,38,50,63,78,95,113,132,154,176,201,227,254,283,314,

%T 346,380,415,452,491,531,572,616,660,707,755,804,855,908,962,1018,

%U 1075,1134,1194,1256,1320,1385,1452,1520,1590,1662,1735,1809,1885,1963,2043,2123,2206,2290,2376

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

%F a(n) ~ Pi * n^2 /4. - _Vaclav Kotesovec_, Apr 03 2024

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

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

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

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Apr 03 2024