A052060 Numbers n such that the digits of 2^n occur with the same frequency.

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

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