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

Author

Chai Wah Wu, Feb 11 2020

Keywords

• nonn
• base
• more

Comments

Conjecture: there are no more terms beyond 229.

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

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