A330024 a(n) = floor(n/z) where z is the number of zeros in the decimal expansion of 2^n, and a(n)=0 when z=0.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 11, 12, 0, 0, 0, 0, 17, 0, 0, 20, 21, 22, 23, 0, 0, 26, 0, 0, 29, 30, 0, 0, 0, 0, 0, 0, 0, 38, 0, 40, 41, 21, 14, 44, 45, 46, 47, 48, 0, 50, 0, 26, 17, 27, 27, 28, 57, 58, 29, 30, 20, 31, 31, 32, 65, 66, 0, 68, 23, 23, 71, 0

Offset

0,11

Comments

Is a(229)=229 the largest term?

a(8949)=41; is 8949 the largest n such that a(n) >= 41?

Is 79391 the largest n such that a(n) <= 30?

Is 30 <= a(n) <= 36 true for all n >= 713789?

Conjecture: For every sequence which can be named as "digit k appears m times in the decimal expansion of 2^n", the sequences are finite for 0 <= k <= 9 and any given m >= 0. Every digit from 0 to 9 are inclined to appear an equal number of times in the decimal expansion of 2^n as n increases.

Links

Metin Sariyar, Table of n, a(n) for n = 0..32000

Formula

Conjecture: a(n) = 33 (= floor(10/log_10(2))) for all sufficiently large n. - Pontus von Brömssen, Jul 23 2021

Example

a(11) = 11 because 2^11 = 2048, there is 1 zero in 2048 and the integer part of 11/1 is 11.

Maple

f:= proc(n) local z;
  z:= numboccur(0, convert(2^n, base, 10));
  if z = 0 then 0 else floor(n/z) fi
end proc:
map(f, [$1..100]); # Robert Israel, Nov 28 2019

Mathematica

Do[z=DigitCount[2^n, 10, 0]; an=IntegerPart[n/z]; If[z==0, Print[0], Print[an]], {n, 0, 8000}]

Prog

(Magma) a:=[0]; for n in [1..72] do z:=Multiplicity(Intseq(2^n), 0); if z ne 0 then  Append(~a, Floor(n/z)); else Append(~a, 0); end if; end for; a; // Marius A. Burtea, Nov 27 2019
(PARI) a(n) = my(z=#select(d->!d, digits(2^n))); if (z, n\z, 0); \\ Michel Marcus, Jan 07 2020
(Python)
def A330024(n):
  z=str(2**n).count('0')
  return n//z if z else 0 # Pontus von Brömssen, Jul 24 2021

Crossrefs

Cf. A007377, A027870.

Sequence in context: A108787 A097585 A063671 * A184992 A162501 A286890

Adjacent sequences: A330021 A330022 A330023 * A330025 A330026 A330027

Keyword

nonn,base

Author

Metin Sariyar, Nov 27 2019

Status

approved