[seqfan] Re: Edit of A155030

Sean A. Irvine sairvin at xtra.co.nz
Fri Oct 9 02:38:44 CEST 2009

```I agree the description is very hard to follow.
However, I don't think 2 should be in A155030 and I think it is different
to A155025.

n=2=prime, prime(2)=3, concatenation is 23 = prime, hence not in A155030.

Similarly,

n=23=prime, prime(23)=83, concatenation is 2383 = prime, hence not in A155030.

But it does look like 19 should be in

n=19=prime, prime(19)=67, concatenation 1967 = composite, 19 should be in A155030.

Sean.

Alonso Del Arte 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[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.
>
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