

A052060


Numbers n such that the digits of 2^n occur with the same frequency.


3



0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 20, 29
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OFFSET

1,3


COMMENTS

Previous name was "Smallest power of 2 whose digits occur with same frequency n".
Next term > 3597.
Not multiplicative since a(18) is supposedly > 3597, but a(2) = 2 and a(9) = 9.  David W. Wilson, Jun 12 2005
From Robert Israel, Aug 14 2015: (Start)
Next term (if any) > 10^4.
It is highly likely that the sequence is finite. For each m, there are at most 4 powers of 2 with m digits. If m is large, of the 9*10^m numbers with m digits, there are at most about c * 10^m/m^(9/2) with equal digit frequencies where c is a constant (this comes from the case where there all 10 digits are represented with frequencies m/10). Thus heuristically the expected number of mdigit powers of 2 with equal digit frequencies decreases like m^(9/2), and this has a finite sum. (End)


LINKS

Table of n, a(n) for n=1..18.


EXAMPLE

E.g., 2^29 = 536870912 where each digit occurs once in this case.


MAPLE

filter:= proc(n) local x, i, P;
P:= add(x^i, i=convert(2^n, base, 10));
nops({coeffs(P, x)})=1
end proc:
select(filter, [$1..10^4]); # Robert Israel, Aug 14 2015


CROSSREFS

Cf. A052069, A052070, A052071, A052072.
Sequence in context: A052057 A252493 A005496 * A084688 A194898 A331271
Adjacent sequences: A052057 A052058 A052059 * A052061 A052062 A052063


KEYWORD

nonn,base,hard,more


AUTHOR

Patrick De Geest, Jan 15 2000


EXTENSIONS

Name and offset corrected by Michel Marcus, Aug 12 2015


STATUS

approved



