# [seqfan] Re: when is 1234...n a prime?

Neil Sloane njasloane at gmail.com
Sun Oct 4 04:34:02 CEST 2015

```My gut feeling is that for all the sequences of this ilk, there
may be an accidental prime or two at the beginning, or not,
but after a while the primes are as rare as pearls in oysters.
Yes, there will be infinitely many primes in any given sequence,
but  they will only appear after a colossal number of steps.

A007908 is a case where there were no "small" terms
(note the quotes!), whereas for the base-2 analog of A007908, which is
A04777,
there IS a small prime, 485398038695407. When is the next prime? I would
like to know.
(See Concatenation of first n numbers in other bases: 2: A047778,
3:A048435, 4: A048436, 5: A048437, 6: A048438, 7: A048439, 8:A048440, 9:
A048441, 10: this sequence, 11: A048442, 12:A048443, 13: A048444, 14:
A048445, 15: A048446, 16: A048447.)

Likewise, for the "concatenate 1 thru n in base 10, but skip 2"
sequence, A262572, two "small" primes appear:

13, 134567891011121314151617181920212223242526272829303132333435363738394041
When is the next?
(See A262571-A262582)

I would be happy to be proved wrong! If there a lot of "small" primes
in any of these it would be a welcome surprise. Welcome because one
hates to be told, yes, there are infinitely many terms in this sequence
(primes in A007908, say) but I'm sorry, you will never see even one of them.

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Email: njasloane at gmail.com

On Sat, Oct 3, 2015 at 5:19 PM, Hans Havermann <gladhobo at teksavvy.com>
wrote:

> Franklin T. Adams-Watters: "I'm interested in what the sequence looks like
> in other bases. Are there other bases where there are none for a long time?"
>
> Based on a not-too-long trial: 4, 13, 18, 19, 22, 25, 26, 28, ...
>
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>
```