# [seqfan] Re: Error in A180269 Primes of the form 3^3+3*n+1

Jonathan Post jvospost3 at gmail.com
Mon Aug 23 23:24:07 CEST 2010

```To be slightly less arbitrary, consider the array A[k,n] = primes of
the form (k^n) + (k*n) + 1, with k, n, positive integers.

This is prime(n+2) for row k=1,
A163115   Primes of the form 2^n+2*n+1.  for row k+2.
Then seq A180269 as corrected for row k=3.
Row 4, well, no values I could spot through (4^100) + (4*100) + 1.

Main diagonal A[n,n] = primes of the form (n^n) + (n^2) + 1
= {3, 43, 37, ...}

On Mon, Aug 23, 2010 at 1:42 PM, Charles Greathouse
<charles.greathouse at case.edu> wrote:
> Good catch.  The sequence should be
> Primes of the form 3^n + 3n + 1.
> and the offset should be 1.
>
> Also, the keyword easy should be removed, since the sequence grows
> exponentially and checking large numbers for primality is hard.
>
> It's probably also worth mentioning the indexes n:
> 0,1,3,41,45,83,95,181,193,195,311,325,901,1825,...
> although I wouldn't submit this as its own sequence.
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
> On Mon, Aug 23, 2010 at 4:32 PM, Jonathan Post <jvospost3 at gmail.com> wrote:
>> A180269 Primes of the form 3^3+3*n+1.
>> But the PARI seems to be for the formula 3^k+3*k+1 instead.
>> The formula as given in the seq's title is equivalent to "Prtimes of
>> the form 27 + 3*n + 1" hence "primes of the form 3*n + 28"
>> which would begin 31, 37, 43, 61, 67, 73, 79, 97, 103, 109, 127, 139, 151, ...
>> which is A002476  Primes of form 6n + 1 for n>3
>> or A002476(n+3)
>> unless I'm also making an elementary mistake.
>>
>>
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```