# [seqfan] Edit of A155030

Alonso Del Arte alonso.delarte at gmail.com
Fri Oct 9 01:56:38 CEST 2009

```I was just about to send Neil Sloane the following edit of A155030 when I
decided to look up my list of terms left out by the original author. The
list, 2, 19, 23, 29, 43, 47, 53, happens to match A155025 by the same
author, so now I'm not sure I understood A155030 correctly. I would
appreciate a second set of eyeballs to confirm or deny that A155025 and
A155030 ought to be merged into one.

Al

%I A155030
%S A155030 2, 5, 11, 17, 19, 23, 29, 31, 41, 43, 47, 53, 67, 71, 73, 79, 89,
97, 101, 107, 109, 127, 131, 137, 139, 157, 163, 167, 173, 191, 193, 211,
223, 227, 229, 233, 239, 241, 257, 277, 281, 293, 307, 311, 313, 317, 331,
337, 347, 349, 359, 367, 373, 379
%N A155030 Primes n such that the base 10 concatenation of pi(n) and that
prime n is composite (with pi being the prime counting function).
%e A155030 The third prime is 5, and the base 10 concatenation of 3 and 5 is
35, which is a composite number; thus 5 is in the sequence. The fourth prime
is 7, and the base 10 concatenation of 4 and 7 is 47, which is a prime; thus
7 is not in the sequence.
%t A155030 Select[Prime[Range[75]],
Not[PrimeQ[FromDigits[Join[IntegerDigits[PrimePi[#]], IntegerDigits[#]]]]]
&]
%Y A155030 Cf. A000027, A000040, A002808.
%Y A155030 Sequence in context: A088046 A155882 A087373 this_sequence
A030468 A085634
A157478
%Y A155030 Adjacent sequences: A155027 A155028 A155029 this_sequence A155031
A155032
A155033
%K A155030 nonn,base
%O A155030 1,1
%A A155030 Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jan 19 2009
%E A155030 According to my understanding of this sequence, and assuming that
the original author was not able to compute elements beyond 67, the
following elements were mistakenly left out by the author: 2, 19, 23, 29,
43, 47, 53. The first prime is 2, and indeed 12 is composite. The  eighth
prime is 19, and we can verify that 819 is a multiple of 3, 7 and 13.
%C A155030 Changing the concatenation to the digits of the prime n first and
then the digits of pi(n) results in a completely different sequence.

```