This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A379140 #11 Dec 16 2024 10:58:23
%S A379140 1,2,8,11,15,16,17,18,21,25,26,30,40,44,46,47,50,51,53,55,60,63,64,74,
%T A379140 77,81,86,88,89,93,95,101,123,130,131,133,134,140,152,154,158,161,164,
%U A379140 166,176,181,189,192,198,209,214,215,233,245,264,268,274,291,293,295,297,324,326,334,352,357
%N A379140 Numbers k such that the greatest prime < 10^k and the least prime > 10^k share no decimal digits.
%C A379140 Charles R Greathouse IV conjectures that A107801(n) = prime(n) for n sufficiently large (and similarly for other related sequences). If that is the case, this sequence must be finite.
%H A379140 Robert Israel, <a href="/A379140/b379140.txt">Table of n, a(n) for n = 1..250</a>
%e A379140 a(3) = 8 is a term because the greatest prime < 10^8 and the least prime > 10^8 are 99999989 and 100000007 respectively, and these have no digits in common.
%e A379140 5 is not a term because the greatest prime < 10^5 and the least prime > 10^5 are 99991 and 100003 respectively, and these have digit 1 in common.
%p A379140 filter:= t -> convert(convert(prevprime(10^t),base,10),set) intersect convert(convert(nextprime(10^t),base,10),set) = {}:
%p A379140 select(filter, [$1..400]);
%Y A379140 Cf. A003617, A003618, A107801.
%K A379140 nonn,base
%O A379140 1,2
%A A379140 _Robert Israel_, Dec 16 2024