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Another number series

Another number series

Posers and Puzzles

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1
3
13
61

What comes next and why?

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Originally posted by brobluto
1
3
13
61

What comes next and why?
65









All are Vegetarian dishes

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I'm gonna go with 26

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Originally posted by forkedknight
I'm gonna go with 26
Why?

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Originally posted by brobluto
Why?
I was trying to think of an expression for it.

using integer division, aka dropping the remainder:
s(n+1) = 10*( s(n-1)/10 + s(n) % 10 ) + s(n)/10

where % is for modulo division

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My guess would be a prime number around 250-260, but I have yet to find any rule which explains how you arrive at each number.

Can we have a hint?

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Originally posted by geepamoogle
My guess would be a prime number around 250-260, but I have yet to find any rule which explains how you arrive at each number.

Can we have a hint?
You're on the right track with prime numbers.

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Originally posted by geepamoogle
My guess would be a prime number around 250-260, but I have yet to find any rule which explains how you arrive at each number.

Can we have a hint?
Coincidence or help? (Obviously 3 does not fit pattern)

1 = (2^2) - 3

13 = (2^4) - 3

61 = (2^6) - 3

Will that help finding your prime?

Is (2^8) - 3 = 253 in series? 🙄

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Originally posted by wolfgang59
Coincidence or help? (Obviously 3 does not fit pattern)

1 = (2^2) - 3

13 = (2^4) - 3

61 = (2^6) - 3

Will that help finding your prime?

Is (2^8) - 3 = 253 in series? 🙄
No, 253 is not in the series.

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I apologize, the series is

1
3
13
71

One being the first prime number (I know that's somewhat debatable, but for this exercise it is)

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Originally posted by brobluto
One being the first prime number (I know that's somewhat debatable, but for this exercise it is)
For "debatable" read "wrong" 🙂

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Originally posted by brobluto
You're on the right track with prime numbers.
Is 1 a prime number?

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Originally posted by Thomaster
Is 1 a prime number?
Not technically, no. But 1 is part of the series and hint. It's as if you started counting 1 through 10, but skipped 2, and 4-12. (although that's not the answer)

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479, the 72nd prime number after 71

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1 is a sort of an oddball.

A prime number has exactly two integer divisors, 1 and itself.
A composite number has 3 or more divisors.

1 only has a singular divisor, itself. It is the only counting number with this property.

For most mathematical purposes, 1 isn't considered 'prime', but rather a multiplicative identity. For instance, 1 isn't listed for prime factorization of a number.

That being said, it would seem for the purposes of this pattern, 1 is considered prime, and as such I will accept it.

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