PARI's commands

[CRGreathouse]

Originally Posted by 3.14159

Oh.

We can construct it similarly to how the Proth numbers are constructed. Should there be a k < b^b restriction? Or do we allow all the 4n + 1 primes in?

My sequences include even b = 1.

Good thought for a third way to do it, though: a sequence of all the primes of the form k*b^b+1, subject to k < b^b.

[3.14159]

Originally Posted by CRGreathouse

Mt sequences include even b = 1.

b can't be 1, or else it would be an exact duplicate of this.

b has to be greater than 2.

[CRGreathouse]

Originally Posted by 3.14159

b can't be 1, or else it would be an exact duplicate of this.

I suppose you didn't understand my suggestions, then, as all three included b = 1 and none of them are the same as A000040.

[3.14159]

Originally Posted by CRGreathouse

I suppose you didn't understand my suggestions, then, as all three included b = 1 and none of them are the same as A000040.

It would in fact be the same because:

(p-1) * 1¹ + 1 = p

And therefore, can be any odd prime number.

[science_man_88]

Originally Posted by CRGreathouse

We need to find a good sequence without arbitrary points. So no minimum of 60 on b and no maximum of 10,000 on k.

I can think of a few ways to do this, but I'll let you decide. One example: consider a two-dimensional array where each row corresponds to a b-value and the values in a row are the least k-values that produce a prime. Then read this array by antidiagonals (or some other reasonable way). The first column is A070855, while the first row is A000040.

Another way: for each prime p, give the largest b value such that there exists a k with k*b^b+1 = p. Then give the values for 2, 3, 5, ....

Maybe both of these are good.


These examples avoid not only the arbitrariness of bounds, but also make ordinary sequences or 'tabl's rather than 'tabf's.

in that case the anti-diagonals read 2,5,3,109 ? Or 2,3,5,109, neither are found in what I'm searching.

[CRGreathouse]

Originally Posted by science_man_88

in that case the anti-diagonals read 2,5,3,109 ? Or 2,3,5,109, neither are found in what I'm searching.

I'm sure neither are in.

The canonical antidiagonal mapping functions for the OEIS are

t1(n)=floor(-1/2+sqrt(2+2*n))
t2(n)=n-binomial(floor(1/2+sqrt(2+2*n)), 2)

so I get
2, 3, 5, 5, 13, 109, 7, 29,163, 257, ...
although flipping rows and columns gives the equally-valid
2, 5, 3, 109, 13, 5, 257, 163, 29, 7, ...
.

[3.14159]

Originally Posted by CRGreathouse

That doesn't match any of my sequences, sorry.

They are irrelevant to what I was discussing.

[3.14159]

If there's no k < b^b restriction, b > 1.

If there is a k < b^b restriction, b ≥ 1.

[CRGreathouse]

Originally Posted by 3.14159

They are irrelevant to what I was discussing.

I was quite precise, actually. Admittedly, I didn't define how to read by antidiagonals, but there's a standard way to do that in the OEIS. But regardless, none of them could be interpreted as A000040 except by a person who thinks "antidiagonal" means "row".

[science_man_88]

Originally Posted by CRGreathouse

I'm sure neither are in.

The canonical antidiagonal mapping functions for the OEIS are

t1(n)=floor(-1/2+sqrt(2+2*n))
t2(n)=n-binomial(floor(1/2+sqrt(2+2*n)), 2)

so I get
2, 3, 5, 5, 13, 109, 7, 29,163, 257, ...
although flipping rows and columns gives the equally-valid
2, 5, 3, 109, 13, 5, 257, 163, 29, 7, ...
.

closest I find is http://www.research.att.com/~njas/sequences/A097453

[3.14159]

Originally Posted by CRGreathouse

I was quite precise, actually. Admittedly, I didn't define how to read by antidiagonals, but there's a standard way to do that in the OEIS. But regardless, none of them could be interpreted as A000040 except by a person who thinks "antidiagonal" means "row".

If there is no k < b^b restriction, and b = 1 is allowed, it is precisely the same as A000040.

I will begin work on the sequence with the k < b^b restriction.