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a(n) is the least positive exponent k such that the decimal expansion of 7^k contains n consecutive zeros.
1

%I #25 Nov 16 2019 02:15:32

%S 1,4,20,74,154,499,510,4411,6984,33836,61282,709339,1570651

%N a(n) is the least positive exponent k such that the decimal expansion of 7^k contains n consecutive zeros.

%e 7^20 = 79792266297612001 is the first power of 7 that has 2 consecutive zeros, so a(2) = 20.

%e 7^74 = 344552147465294110719732986332367243247925798357929806000836849 is the first power of 7 that has 3 consecutive zeros, so a(3) = 74.

%t Print[1]; zero = {}; Do[zero = zero <> "0"; k = 1; While[StringPosition[ToString[7^k], zero] == {}, k++]; Print[k];, {n, 1, 10}]

%Y Cf. A006889 (2^k), A195269 (3^k), A329172 (5^k).

%K nonn,base,more,hard

%O 0,2

%A _Vaclav Kotesovec_, Nov 07 2019

%E a(12) from _Chai Wah Wu_, Nov 13 2019