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

1,1

Comments

Conjecture: there are no more terms beyond 229.

Links

Table of n, a(n) for n=1..26.

Example

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.

Prog

(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

Crossrefs

Cf. A320601.

Sequence in context: A175389 A350779 A280591 * A332226 A338590 A003333

Adjacent sequences: A308688 A308689 A308690 * A308692 A308693 A308694

Keyword

nonn,base,more

Author

Chai Wah Wu, Feb 11 2020

Status

approved