A072098 Numbers k such that the difference between 10^k and the next prime > 10^k is a record high.
1, 3, 7, 12, 16, 21, 28, 62, 97, 118, 122, 135, 164, 218, 333, 346, 387, 443, 485, 521, 630, 819
Offset: 1
Examples
For a(22)=819 the difference is 10443 and no other n <= 827 exceeds that difference.
Programs
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Mathematica
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}]