# [seqfan] Re: Sum of a binary power and an odd prime power

Ray Chandler rayjchandler at sbcglobal.net
Fri Apr 16 16:35:01 CEST 2010

```Given the examples, comments and formulas, I read the intent to be

%N A115230 Number of ways to write the n-th prime as a sum
of a binary power (A000079) and an odd prime power (A061345).

But the terms of A115230 are not consistent with that.

I think they are just wrong and the three sequences derived from them as well.

Ray Chandler

> No, not consistent.  Odd multiples of p^k for p odd prime and
> k >= 1 give the odd numbers except for 1, so that would be
> something like A035100 (apart from the first term).
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
> On Fri, Apr 16, 2010 at 7:26 AM, N. J. A. Sloane
> <njas at research.att.com> wrote:
> > Charles said:
> > Would someone check sequences A115230, A115231, A115232,
> and A115230?
> >
> > Me:  One suggestion is that A115230, which presently reads
> >
> > %N A115230 Number of ways to write the n-th prime as a sum
> of a binary power and an odd prime power.
> >
> > should really be
> >
> > %N A115230 Number of ways to write the n-th prime as a sum
> of a power of 2 and an odd multiple of a (prime or a power of
> a prime).
> >
> > That is, number of ways to write prime(n) as 2^i + j*p^k
> where i >= 0,
> > k >= 1, j is odd and >= 1, and p is a prime.
> >
> > Could you check if that is consistent with the entries?
> >
> > Neil

```