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.
10, 17, 20, 26, 29, 30, 38, 40, 44, 47, 50, 57, 65, 68, 71, 74, 84, 95, 122, 124, 129, 130, 149, 151, 184, 229
Offset: 1
Examples
For the first 10 terms of A320601, the fractions of 0's among the decimal digits of 2^k are: 2^10 = 1024, fraction of 0's = 1/4 2^11 = 2048, fraction of 0's = 1/4 2^12 = 4096, fraction of 0's = 1/4 2^17 = 131072, fraction of 0's = 1/6 2^20 = 1048576, fraction of 0's = 1/7 2^21 = 2097152, fraction of 0's = 1/7 2^22 = 4194304, fraction of 0's = 1/7 2^23 = 8388608, fraction of 0's = 1/7 2^26 = 67108864, fraction of 0's = 1/8 2^29 = 536870912, fraction of 0's = 1/9 So record minima are reached at k = 10, 17, 20, 26 and 29.
Crossrefs
Cf. A320601.
Programs
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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
Comments