Timeline for Smallest Harmonic number greater than N
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 12 at 7:01 | comment | added | noodle person | Nice, that makes sense, thank you for explaining. | |
| Jun 12 at 0:06 | comment | added | Ka Wa Yip | @noodleperson \$T_k\$ always goes up as \$k\$ increases (since one just keeping adding \$1/2\$ to it), while \$N\$ is given. One can choose a \$k\$ to satisfy \$T_k > N\$: for example, \$T_{2^{2N}} > N\$ . Let's say \$N = 3/2\$. \$2^{2(3/2)}=8\$. \$T_{8} = 1 + 1/2 +1/2+1/2 = 1+3/2 > 3/2\$. Since the input \$N\$ is an integer, a equivalent way to think about it is \$T_{2^{N}} > N/2\$. This is true because of the extra "1" at the beginning of \$T_k\$. | |
| Jun 11 at 21:37 | comment | added | noodle person | Welcome to CGCC, nice first submission, and clever way of approaching this! I see \$ T_k > N \$ implies \$ H_k > N \$ but what if \$ H_k > N > T_k \$? Or does that case just never happen in this sequence? | |
| S Jun 11 at 20:36 | review | First answers | |||
| Jun 12 at 10:57 | |||||
| S Jun 11 at 20:36 | history | answered | Ka Wa Yip | CC BY-SA 4.0 |