A329174 a(n) is the least positive exponent k such that the decimal expansion of 7^k contains n consecutive zeros.
1, 4, 20, 74, 154, 499, 510, 4411, 6984, 33836, 61282, 709339, 1570651
Offset: 0
Examples
7^20 = 79792266297612001 is the first power of 7 that has 2 consecutive zeros, so a(2) = 20. 7^74 = 344552147465294110719732986332367243247925798357929806000836849 is the first power of 7 that has 3 consecutive zeros, so a(3) = 74.
Programs
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Mathematica
Print[1]; zero = {}; Do[zero = zero <> "0"; k = 1; While[StringPosition[ToString[7^k], zero] == {}, k++]; Print[k];, {n, 1, 10}]
Extensions
a(12) from Chai Wah Wu, Nov 13 2019