u/Super_M13

Detention for you

Here's the other side of this pattern:

https://preview.redd.it/rui373gqc8yh1.png?width=1016&format=png&auto=webp&s=34e9c06dcdecae153de67626cf61b763bfefadcd

Day 198 of linking the daily natural number to 13:

198 is the 13th number n such that n²+13 and n²+13² are primes:

2, 10, 12, 28, 42, 60, 68, 108, 110, 122, 142, 180, 198, ... (OEIS A176978)

198²+13=39217 (4129th prime number) and 198²+13²=39373 (4146th prime number)

Darn

Darn

Day 197 of linking the daily natural number to 13:

197 is the 13th prime which is palindrome in 3 or more bases (OEIS A087166):

1. 17 = 11₁₆=101₄=10001₂
2. 31 = 11₃₀=111₅=11111₂
3. 67 = 11₆₆=151₆=232₅
4. 73 = 11₇₂=111₈=1001001₂
5. 107 = 11₁₀₆=212₇=1101011₂
6. 109 = 11₁₀₈=131₉=414₅
7. 127 = 11₁₂₆=151₉=1111111₂
8. 151 = 11₁₅₀=151₁₀=12121₃
9. 157 = 11₁₅₆=111₁₂=313₇
10. 173 = 11₁₇₂=212₉=20102₃
11. 181 = 11₁₈₀=131₁₂=181₁₀
12. 191 = 11₁₉₀=191₁₀=232₉=515₆
13. 197 = 11₁₉₆=101₁₄=525₆

Darn

Darn

Here's how I made this pattern:

https://preview.redd.it/lqzs7oxo4uxh1.png?width=1037&format=png&auto=webp&s=9b0d7be2dd3f16181bfb16e20a7a048cec375604

Day 196 of linking the daily natural number to 13:

196 is the 13th natural number whose number of divisors is a power of an odd prime:

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 169, 196, ... (OEIS A387918)

196 has 3² divisors: 1, 2, 4, 7, 14, 28, 49, 98, 196

Happy cake day!

Darn

Darn

Day 195 of linking the daily natural number to 13:

195 is the 13th number representable as x^y×y+y, where x>1 and y>1 are integers (OEIS A249989):

1. 10=2²×2+2
2. 20=3²×2+2
3. 27=2³×3+3
4. 34=4²×2+2
5. 52=5²×2+2
6. 68=2⁴×4+4
7. 74=6²×2+2
8. 84=3³×3+3
9. 100=7²×2+2
10. 130=8²×2+2
11. 164=9²×2+2
12. 165=2⁵×5+5
13. 195=4³×3+3

Also, 195=13×15

Darn

A lot of people use Ganger as well. It's basically Headman but faster drones in exchange for a slower reload.

Darn

Day 194 of linking the daily natural number to 13:

194 is the 13th number k such that φ(σ(k)) divides σ(φ(k)):

1, 7, 9, 29, 71, 97, 109, 121, 139, 142, 175, 183, 194, ... (OEIS A066930)

φ(σ(194))=φ(294)=84 and σ(φ(194))=σ(96)=252; 252/84=3.

Darn

Darn

Day 193 of linking the daily natural number to 13:

193 is the 13th lucky prime:

3, 7, 13, 31, 37, 43, 67, 73, 79, 127, 151, 163, 193, ... (OEIS A031157)

Darn

Darn

Hexa-Machine has 14 upgrade paths:

Twin -> Hexa Tank -> Hexa-Trapper -> Hexa-Machine
Twin -> Wark -> Hexa-Trapper -> Hexa-Machine
Twin -> Wark -> Expeller -> Hexa-Machine
Machine Gun -> Machine Trapper -> Tri-Machine -> Hexa-Machine
Machine Gun -> Machine Trapper -> Expeller -> Hexa-Machine
Flank Guard -> Hexa Tank -> Hexa-Trapper -> Hexa-Machine
Flank Guard -> Tri-Trapper -> Hexa-Trapper -> Hexa-Machine
Flank Guard -> Tri-Trapper -> Tri-Machine -> Hexa-Machine
Trapper -> Tri-Trapper -> Hexa-Trapper -> Hexa-Machine
Trapper -> Tri-Trapper -> Tri-Machine -> Hexa-Machine
Trapper -> Machine Trapper -> Tri-Machine -> Hexa-Machine
Trapper -> Machine Trapper -> Expeller -> Hexa-Machine
Trapper -> Wark -> Hexa-Trapper -> Hexa-Machine
Trapper -> Wark -> Expeller -> Hexa-Machine

Day 192 of linking the daily natural number to 13:

192 is the smallest natural number with exactly 13 proper divisors:

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96