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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. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A079630 A175389 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

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Last modified April 10 11:32 EDT 2021. Contains 342845 sequences. (Running on oeis4.)