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

0,2

Links

Table of n, a(n) for n=0..12.

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A197426 A061981 A054611 * A057333 A196432 A302815

Adjacent sequences: A329171 A329172 A329173 * A329175 A329176 A329177

Keyword

nonn,base,more,hard

Author

Vaclav Kotesovec, Nov 07 2019

Extensions

a(12) from Chai Wah Wu, Nov 13 2019

Status

approved