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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 (list; graph; refs; listen; history; text; internal format)
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 m-digit 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

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Last modified October 5 09:00 EDT 2022. Contains 357252 sequences. (Running on oeis4.)