cp's OEIS Frontend

A308691 Numbers k in A320601 such that the fraction of the number of zeros in the decimal expansion of 2^k reaches a record minimum.

%I A308691 #30 Feb 15 2020 10:42:39
%S A308691 10,17,20,26,29,30,38,40,44,47,50,57,65,68,71,74,84,95,122,124,129,
%T A308691 130,149,151,184,229
%N A308691 Numbers k in A320601 such that the fraction of the number of zeros in the decimal expansion of 2^k reaches a record minimum.
%C A308691 Conjecture: there are no more terms beyond 229.
%e A308691 For the first 10 terms of A320601, the fractions of 0's among the decimal digits of 2^k are:
%e A308691   2^10 =      1024, fraction of 0's = 1/4
%e A308691   2^11 =      2048, fraction of 0's = 1/4
%e A308691   2^12 =      4096, fraction of 0's = 1/4
%e A308691   2^17 =    131072, fraction of 0's = 1/6
%e A308691   2^20 =   1048576, fraction of 0's = 1/7
%e A308691   2^21 =   2097152, fraction of 0's = 1/7
%e A308691   2^22 =   4194304, fraction of 0's = 1/7
%e A308691   2^23 =   8388608, fraction of 0's = 1/7
%e A308691   2^26 =  67108864, fraction of 0's = 1/8
%e A308691   2^29 = 536870912, fraction of 0's = 1/9
%e A308691 So record minima are reached at k = 10, 17, 20, 26 and 29.
%o A308691 (PARI) lista(nn) = {my(kmin = oo, d, k); for(n=1, nn, d = digits(2^n); if (! vecmin(d), if ((k = #select(x->(x==0), d)/#d) < kmin, print1(n, ", "); kmin = k);););} \\ _Michel Marcus_, Feb 15 2020
%Y A308691 Cf. A320601.
%K A308691 nonn,base,more
%O A308691 1,1
%A A308691 _Chai Wah Wu_, Feb 11 2020