# Composites, emirps, and emirpimes among de Polignac numbers (A006285)

Roland Bacher Roland.Bacher at ujf-grenoble.fr
Thu Jun 19 08:25:13 CEST 2008

```Dear Jonathan Post,

Your title for a message to the sequence-fan list is
slightly unfortunate, the word "emirps" sounds like a spam.

Ideally, a title should be short and contain clearly
identifiable and well-established words (exple: contain
the word "sequence(s)").

This allows a fast scan of the mails without any risk of

Sorry for this not strictly mathematical message but
information overflow becomes an encreasing problem of
our time.

I have no remarks concerning your sequence except that
I share Neil's thougths.

Best whishes, Roland Bacher

On Wed, Jun 18, 2008 at 09:34:15PM -0700, Jonathan Post wrote:
> Emirps (A006567) which are also de Polignac numbers (A006285).
>
> 149, 337, 701, 907, 1259, 1597, 1619, 1657, 1867
>
> I think that njas dislikes emirps (or the name of them).  But this is
> a sequence that I'd be tempted to submit, if anyone else thinks that's
> worthwhile.
>
> I also note that A006285(14) = 905 = 5 * 181 is the first composite in
> that sequence. Law of small numbers can fool one into thinking them
> all noncompiste, as the first 13 are. Next composites are:
> A006285(16) = 959 = 7 * 137
> A006285(21) = 1199 = 11 * 109
> A006285(22) = 1207 = 17 * 71
> A006285(23) = 1211 = 7 * 173 which, reversed, is 1121 = 19 * 59, hence
> 1211 is the smallest emirpimes (A097393) among the de Polignac
> numbers.
> A006285(24) = 1243 = 11 * 113 which, reversed is 3421 = 11 * 311, so emirpimes
> A006285(26) = 1271 = 31 * 41
> A006285(27) = 1477 = 7 * 211
> A006285(28) = 1529 = 11 * 139
> A006285(29) = 1541 = 23 * 67
> A006285(31) = 1589 = 7 * 227
> A006285(34) = 1649 = 17 * 97
>
> Note that A006285(36) = 1719 = 3^2 * 191 is the first value with 3
> prime factors (with multiplicity).
>
> A006285(40) = 1807 = 13 * 139, reversed is 7081 = 73 * 97 so emirpimes...
>
> Again, I know that njas and many others dislike "base" sequences.
> But, to me, the intersection of two OEIS seqs is (if not too sparse) a
> legitimate submission.
>
> Anyone have an opinion on this? Or an extension?
>
> I feel that I've been well-behaved, in having earlier today submitted
> 3 seqs from arXiv papers in Math and Physics.  Sometimes I want to
> just swim in the shallow end of the pool...
>
> Best,
>
> Jonathan Vos Post

```