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

Jonathan Post jvospost3 at gmail.com
Thu Jun 19 06:34:15 CEST 2008

```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

```