%I #7 Sep 03 2024 16:12:34
%S 1,3,7,12,16,21,28,62,97,118,122,135,164,218,333,346,387,443,485,521,
%T 630,819
%N Numbers k such that the difference between 10^k and the next prime > 10^k is a record high.
%e For a(22)=819 the difference is 10443 and no other n <= 827 exceeds that difference.
%t NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; d = 0; k = 1; Do[ While[f = NextPrim[10^k] - 10^k; d >= f, k++ ]; d = f; Print[k], {n, 1, 50}]
%Y Cf. A038805, A033873.
%K hard,nonn,more
%O 1,2
%A _Robert G. Wilson v_, Jun 18 2002