# [seqfan] Re: Edit of A155030

Maximilian Hasler maximilian.hasler at gmail.com
Fri Oct 9 02:23:12 CEST 2009

```oops, sorry for several confusing permutations of  n and p in the %N
lines in the previous message, here's what I meant to say:

I think they are intended to be different, as given below:
(the %N lines are a bit overloaded in xref's, delete whatever you prefer ;-)

%N A155025 List of primes  p=prime(n)=A000040(n)  such that
n=primepi(p)=A000720(p)  and concat(n, p)=A045532(n) both are
composite.

%o A155025 (PARI)
n=0;forprime(p=1,999, !isprime(n++) && !isprime(eval(Str(n,p))) && print1(p","))

%s A155025
2,19,23,29,43,47,53,71,73,79,89,97,101,107,131,137,139,
163,167,173,193,223,227,229,233,239,257,281,293,307,
311,313,317,337,347,349,359,373,379,383,389,397,409

and the distinct

%N A155030 List of primes p=prime(n)=A000040(n) such that
n=primepi(p)=A000720(p)  is prime and concat(n,p)=A045532(n) is
composite.

%o A155030 (PARI)
n=0;forprime(p=1,999, isprime(n++) && !isprime(eval(Str(n,p))) && print1(p","))

%s A155030
5,11,17,31,41,67,109,127,157,191,211,241,277,
331,367,401,461,509,547,563,587,599,617,739,
773,797,859,877,919,967,991,

Maximilian

On Thu, Oct 8, 2009 at 7:56 PM, Alonso Del Arte
<alonso.delarte at gmail.com> wrote:
> 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],
> 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.
>
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>
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>

```

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