What comes next in these sequences?

[davee123]

Just futzing around, this sequence was suprisingly patterned for the first 8 numbers, then became erratic:

1, 1, 3, 3, 9, 9, 15, 15, 17, 27, ?

And for the sake of more fooling around, this one just popped into my head:

1, 2, 4, 6, 16, 18, 64, 66, 100, 112, ?

DaveE

 

[davee123]

Hm... perhaps hints are in order?

1, 1, 3, 3, 9, 9, 15, 15, 17, 27, ?

Hint: Think primes!

1, 2, 4, 6, 16, 18, 64, 66, 100, 112, ?

Hint: Think factors!
(and you might not want to bother trying to find the next number in the sequence, if going by hand)

DaveE

 

[rhj23]

is the second sequence something like:

a(n) = the smallest number with n distinct factors (this would explain the odd-numbered terms being squares)

havent looked at the first one yet, but the second jumped out at me

 

[davee123]

is the second sequence something like:

a(n) = the smallest number with n distinct factors (this would explain the odd-numbered terms being squares)

havent looked at the first one yet, but the second jumped out at me

Yep! Or, close enough. The smallest number with n distinct factors that's larger than a(n-1). Nice job! Now for the 1st one!

DaveE

 

[siddharth]

Is the first sequence:

a(n) = 2* nth prime number - (n+1)th prime number ?

 

[davee123]

Is the first sequence:

a(n) = 2* nth prime number - (n+1)th prime number ?

Bingo!

DaveE