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Least k such that 3^k has exactly n consecutive 8's in its decimal representation.
9

%I #16 Mar 24 2019 08:07:48

%S 4,23,32,215,1261,538,4797,17612,32311,375482,512959,1847532,8295710,

%T 8885853,80798025

%N Least k such that 3^k has exactly n consecutive 8's in its decimal representation.

%C No more terms < 10^8. - _Bert Dobbelaere_, Mar 20 2019

%e a(3)=32 because 3^32 (i.e., 1853020188851841) is the smallest power of 3 to contain a run of 3 consecutive eights in its decimal form.

%t a = ""; Do[ a = StringJoin[a, "8"]; b = StringJoin[a, "8"]; k = 1; While[ StringPosition[ ToString[3^k], a] == {} || StringPosition[ ToString[3^k], b] != {}, k++ ]; Print[k], {n, 1, 10} ]

%Y Cf. A195269, A131552, A131551, A131550, A131549, A131548, A131547, A131546, A131544.

%K more,nonn,base

%O 1,1

%A _Shyam Sunder Gupta_, Aug 26 2007

%E a(11)-a(14) from _Lars Blomberg_, Feb 02 2013

%E a(15) from _Bert Dobbelaere_, Mar 20 2019