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
KEYWORD
nonn,base
AUTHOR
Metin Sariyar, Nov 27 2019
STATUS
approved