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 3 I stuttered! edited Jul 7 '17 at 22:19 Peregrine Rook 4,84922 gold badges2121 silver badges4040 bronze badges The requested numbers are $$\mathbf{158,~~ 190},~~ 212,~~ 224,~~ 246,~~ 278,~~ 310,~~ 322,~~ \mathbf{354,~~ 376}$$ The formula for the n th Uncle number, $$U_n$$, is $$U_n = 5\times p_n + 2\times n - 19$$ where $$p_n$$ is the n th prime.  The numbers shown in the question are $$U_{13} = 5\times41 + 2\times13 - 19 = 212$$  through  $$U_{18} = 5\times61 + 2\times18 - 19 = 322$$ For completeness, I could explain that $$U_{1} ~~= 5\times2~ ~+ 2\times1~ ~- 19 = 5\times2 ~+~ 2\times1 ~-~ 19 = 10 + 2 - 19 = -7$$ $$U_{1} ~~= 5\times2~ ~+ 2\times1~ ~- 19 = 10 + 2 - 19 = -7$$ How did I figure that out? We have a monotonically increasing sequence of integers that begins with an odd number, but it appears to settle into a groove of being all even numbers.  That made me think: that’s one bit off from a monotonically increasing sequence of integers that begins with an even number, but settles into a groove of being all odd numbers. Hint #3 mentions some parameters regarding grandmother’s home. And, having solved the problem and written the solution, I took another look and noticed that the question body mentions the word “prime”: … watching a prime time show. Looking at the question’s edit history, I see that Hint #1 originally said, “Is in the first para.  Tricky and you need to look around.” but that was edited out. The requested numbers are $$\mathbf{158,~~ 190},~~ 212,~~ 224,~~ 246,~~ 278,~~ 310,~~ 322,~~ \mathbf{354,~~ 376}$$ The formula for the n th Uncle number, $$U_n$$, is $$U_n = 5\times p_n + 2\times n - 19$$ where $$p_n$$ is the n th prime.  The numbers shown in the question are $$U_{13} = 5\times41 + 2\times13 - 19 = 212$$  through  $$U_{18} = 5\times61 + 2\times18 - 19 = 322$$ For completeness, I could explain that $$U_{1} ~~= 5\times2~ ~+ 2\times1~ ~- 19 = 5\times2 ~+~ 2\times1 ~-~ 19 = 10 + 2 - 19 = -7$$ How did I figure that out? We have a monotonically increasing sequence of integers that begins with an odd number, but it appears to settle into a groove of being all even numbers.  That made me think: that’s one bit off from a monotonically increasing sequence of integers that begins with an even number, but settles into a groove of being all odd numbers. Hint #3 mentions some parameters regarding grandmother’s home. And, having solved the problem and written the solution, I took another look and noticed that the question body mentions the word “prime”: … watching a prime time show. Looking at the question’s edit history, I see that Hint #1 originally said, “Is in the first para.  Tricky and you need to look around.” but that was edited out. The requested numbers are $$\mathbf{158,~~ 190},~~ 212,~~ 224,~~ 246,~~ 278,~~ 310,~~ 322,~~ \mathbf{354,~~ 376}$$ The formula for the n th Uncle number, $$U_n$$, is $$U_n = 5\times p_n + 2\times n - 19$$ where $$p_n$$ is the n th prime.  The numbers shown in the question are $$U_{13} = 5\times41 + 2\times13 - 19 = 212$$  through  $$U_{18} = 5\times61 + 2\times18 - 19 = 322$$ For completeness, I could explain that $$U_{1} ~~= 5\times2~ ~+ 2\times1~ ~- 19 = 10 + 2 - 19 = -7$$ How did I figure that out? We have a monotonically increasing sequence of integers that begins with an odd number, but it appears to settle into a groove of being all even numbers.  That made me think: that’s one bit off from a monotonically increasing sequence of integers that begins with an even number, but settles into a groove of being all odd numbers. Hint #3 mentions some parameters regarding grandmother’s home. And, having solved the problem and written the solution, I took another look and noticed that the question body mentions the word “prime”: … watching a prime time show. Looking at the question’s edit history, I see that Hint #1 originally said, “Is in the first para.  Tricky and you need to look around.” but that was edited out. 2 Demonstrated that my series begins with −7. edited Jul 7 '17 at 22:13 Peregrine Rook 4,84922 gold badges2121 silver badges4040 bronze badges The requested numbers are $$\mathbf{158,~~ 190},~~ 212,~~ 224,~~ 246,~~ 278,~~ 310,~~ 322,~~ \mathbf{354,~~ 376}$$ The formula for the n th Uncle number, $$U_n$$, is $$U_n = 5\times p_n + 2\times n - 19$$ where $$p_n$$ is the n th prime.  The numbers shown in the question are $$U_{13} = 5\times41 + 2\times13 - 19 = 212$$  through  $$U_{18} = 5\times61 + 2\times18 - 19 = 322$$ For completeness, I could explain that $$U_{1} ~~= 5\times2~ ~+ 2\times1~ ~- 19 = 5\times2 ~+~ 2\times1 ~-~ 19 = 10 + 2 - 19 = -7$$ How did I figure that out? We have a monotonically increasing sequence of integers that begins with an odd number, but it appears to settle into a groove of being all even numbers.  That made me think: that’s one bit off from a monotonically increasing sequence of integers that begins with an even number, but settles into a groove of being all odd numbers. Hint #3 mentions some parameters regarding grandmother’s home. And, having solved the problem and written the solution, I took another look and noticed that the question body mentions the word “prime”: … watching a prime time show. Looking at the question’s edit history, I see that Hint #1 originally said, “Is in the first para.  Tricky and you need to look around.” but that was edited out. The requested numbers are $$\mathbf{158,~~ 190},~~ 212,~~ 224,~~ 246,~~ 278,~~ 310,~~ 322,~~ \mathbf{354,~~ 376}$$ The formula for the n th Uncle number, $$U_n$$, is $$U_n = 5\times p_n + 2\times n - 19$$ where $$p_n$$ is the n th prime.  The numbers shown in the question are $$U_{13} = 5\times41 + 2\times13 - 19 = 212$$  through  $$U_{18} = 5\times61 + 2\times18 - 19 = 322$$ How did I figure that out? We have a monotonically increasing sequence of integers that begins with an odd number, but it appears to settle into a groove of being all even numbers.  That made me think: that’s one bit off from a monotonically increasing sequence of integers that begins with an even number, but settles into a groove of being all odd numbers. Hint #3 mentions some parameters regarding grandmother’s home. And, having solved the problem and written the solution, I took another look and noticed that the question body mentions the word “prime”: … watching a prime time show. Looking at the question’s edit history, I see that Hint #1 originally said, “Is in the first para.  Tricky and you need to look around.” but that was edited out. The requested numbers are $$\mathbf{158,~~ 190},~~ 212,~~ 224,~~ 246,~~ 278,~~ 310,~~ 322,~~ \mathbf{354,~~ 376}$$ The formula for the n th Uncle number, $$U_n$$, is $$U_n = 5\times p_n + 2\times n - 19$$ where $$p_n$$ is the n th prime.  The numbers shown in the question are $$U_{13} = 5\times41 + 2\times13 - 19 = 212$$  through  $$U_{18} = 5\times61 + 2\times18 - 19 = 322$$ For completeness, I could explain that $$U_{1} ~~= 5\times2~ ~+ 2\times1~ ~- 19 = 5\times2 ~+~ 2\times1 ~-~ 19 = 10 + 2 - 19 = -7$$ How did I figure that out? We have a monotonically increasing sequence of integers that begins with an odd number, but it appears to settle into a groove of being all even numbers.  That made me think: that’s one bit off from a monotonically increasing sequence of integers that begins with an even number, but settles into a groove of being all odd numbers. Hint #3 mentions some parameters regarding grandmother’s home. And, having solved the problem and written the solution, I took another look and noticed that the question body mentions the word “prime”: … watching a prime time show. Looking at the question’s edit history, I see that Hint #1 originally said, “Is in the first para.  Tricky and you need to look around.” but that was edited out. 1 answered Jul 7 '17 at 19:41 Peregrine Rook 4,84922 gold badges2121 silver badges4040 bronze badges The requested numbers are $$\mathbf{158,~~ 190},~~ 212,~~ 224,~~ 246,~~ 278,~~ 310,~~ 322,~~ \mathbf{354,~~ 376}$$ The formula for the n th Uncle number, $$U_n$$, is $$U_n = 5\times p_n + 2\times n - 19$$ where $$p_n$$ is the n th prime.  The numbers shown in the question are $$U_{13} = 5\times41 + 2\times13 - 19 = 212$$  through  $$U_{18} = 5\times61 + 2\times18 - 19 = 322$$ How did I figure that out? We have a monotonically increasing sequence of integers that begins with an odd number, but it appears to settle into a groove of being all even numbers.  That made me think: that’s one bit off from a monotonically increasing sequence of integers that begins with an even number, but settles into a groove of being all odd numbers. Hint #3 mentions some parameters regarding grandmother’s home. And, having solved the problem and written the solution, I took another look and noticed that the question body mentions the word “prime”: … watching a prime time show. Looking at the question’s edit history, I see that Hint #1 originally said, “Is in the first para.  Tricky and you need to look around.” but that was edited out.