[seqfan] fuzzy thinking on my part

Neil Sloane njasloane at gmail.com
Sat Sep 19 03:32:13 CEST 2015


Dear SeqFans, I made a foolish assertion in A262283 which Franklin
and Alois politely corrected. Perhaps the collective wisdom of
this mailing list can straighten things out.

A262283 is based on an old sequence of Amarnath Murthy, A089755,
which Franklin recently noticed was either wrong or needed a better
definition.

A262283, which is the simplest version of Murthy's sequence, starts
2, 3, 5, 7, 11, 13, 31, 17, 71, 19, 97, ..
with the following definition:
a(1)=2. For n>1, let s denote the digit-string of a(n-1) with the first
digit omitted. Then a(n) is the smallest prime not yet present which starts
with s.

The question is, does every prime appear?  The answer is surely NO!
But is there a proof that 23 (say) never appears? I thought this was
obvious, but I was wrong. We might see 7000....00023 eventually,
in which case the next term would be 23.

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.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


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