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%I #30 Feb 15 2020 10:42:39
%S 10,17,20,26,29,30,38,40,44,47,50,57,65,68,71,74,84,95,122,124,129,
%T 130,149,151,184,229
%N 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 Conjecture: there are no more terms beyond 229.
%e For the first 10 terms of A320601, the fractions of 0's among the decimal digits of 2^k are:
%e 2^10 = 1024, fraction of 0's = 1/4
%e 2^11 = 2048, fraction of 0's = 1/4
%e 2^12 = 4096, fraction of 0's = 1/4
%e 2^17 = 131072, fraction of 0's = 1/6
%e 2^20 = 1048576, fraction of 0's = 1/7
%e 2^21 = 2097152, fraction of 0's = 1/7
%e 2^22 = 4194304, fraction of 0's = 1/7
%e 2^23 = 8388608, fraction of 0's = 1/7
%e 2^26 = 67108864, fraction of 0's = 1/8
%e 2^29 = 536870912, fraction of 0's = 1/9
%e So record minima are reached at k = 10, 17, 20, 26 and 29.
%o (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 Cf. A320601.
%K nonn,base,more
%O 1,1
%A _Chai Wah Wu_, Feb 11 2020
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