Another number series

1
3
13
61

What comes next and why?

Originally posted by brobluto
1
3
13
61

What comes next and why?

65









All are Vegetarian dishes

I'm gonna go with 26

Originally posted by forkedknight
I'm gonna go with 26

Why?

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

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?

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.

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? 🙄

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.

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)

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" 🙂

Originally posted by brobluto
You're on the right track with prime numbers.

Is 1 a prime number?

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)

479, the 72nd prime number after 71

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.