# [seqfan] Re: Primes embedded

N. J. A. Sloane njas at research.att.com
Sun May 16 05:55:26 CEST 2010

```Eric Angelini suggested this two weeks ago, but I have
only now had a chance to study it:

a(n) > a(n-1) and a(n) is the smallest available composite
embedding the smallest not yet embedded prime:

S=12,30,35,57,110,130,170,190,230,290,310,370,410,430,447,451,...
p= 2 3   5  7 11  13  17  19  23  29  31  37  41  43   47  51 ...

I see that it met with vigorous opposition.

But allow me to defend it!  I have spent the past 11 hours
processing submissions and edits and emails about sequences,
and it is pretty tough going.   Almost every sequence I looked at
needed work, and I looked at a LOT of sequences today.
It was a a pretty humorless day.

On the other hand, this one made me laugh.  So in spite of
the objections, I am not only going to add it, I'm also

%I A144565
%S A144565 12,30,35,57,110,130,170,190,230,290,310,370,410,430,447,451
%N A144565 a(n) = smallest composite number > a(n-1) that contains the n-th prime as a substring.
%O A144565 1,1
%K A144565 nonn,base,more
%Y A144565 Cf. A169798.
%e A144565 S = 12,30,35,57,110,130,170,190,230,290,310,370,410,430,447,451,...
%e A144565 p = .2.3...5..7.11..13..17..19..23..29..31..37..41..43...47..51....
%A A144565 Eric Angelini, May 01 2010

%I A169798
%S A169798 41,61,83,89,101,127,149,151,163,181,2003,2111
%N A169798 a(n) = smallest prime number > a(n-1) that contains the n-th composite number as a substring.
%O A169798 1,1
%K A169798 nonn,base,more
%Y A169798 Cf. A144565.
%A A169798 N. J. A. Sloane (njas(AT)research.att.com), May 15 2010

Besides, these could easily appear on some IQ test one day.

Neil

```