A052060 -id:A052060 - cp's OEIS frontend

A045540 Numbers whose square contains an equal number of each digit that it contains.

1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 14, 16, 17, 18, 19, 23, 24, 25, 27, 28, 29, 31, 32, 33, 36, 37, 42, 43, 44, 48, 49, 51, 52, 53, 54, 55, 57, 59, 61, 64, 66, 69, 71, 72, 73, 74, 78, 79, 82, 84, 86, 87, 88, 89, 93, 95, 96, 98, 99, 113, 116, 117, 118, 124, 126, 128, 133, 134, 136

Offset: 1

Erich Friedman

The sequence is expected to be infinite. Heuristically, if m is divisible by 10 there should be approximately constant * 10^(m/2)/m^(9/2) m-digit squares where all 10 digits have frequency m/10. - Robert Israel, Aug 14 2015

Robert Israel, Table of n, a(n) for n = 1..3000
P. De Geest, Numbers whose digits occur with same frequency

Cf. A052046, A052047, A052048, A052049, A052050, A052051, A052052, A052060.

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

t={}; Do[If[Length[DeleteDuplicates[Transpose[Tally[IntegerDigits[n^2]]][[2]]]]==1,AppendTo[t,n]],{n,136}]; t (* Jayanta Basu, May 10 2013 *)

A084688 Nonnegative integers n such that 2^n uses only distinct decimal digits.

Original entry on oeis.org

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

Offset: 1

Zak Seidov, Jul 01 2003

There are exactly 18 numbers such that 2^n uses only distinct digits.
a(n) can have at most 10 digits. As 2^34 has 11 digits, a(n) < 34. - David A. Corneth, Aug 03 2015
Subsequence of A052060. - R. J. Mathar, Sep 17 2008

			29 is the last term with 2^29 = 536870912 = A260814(18). - _Zak Seidov_, Aug 02 2015

Cf. A000079, A260814, A052060.

Select[Range[0, 34], Max@ DigitCount[2^#] == 1 &] (* Michael De Vlieger, Aug 03 2015 *) (* with corrections by Zak Seidov, Aug 05 2015 *)

lista() = {lim = ceil(log(10^11)/(log(2)));for (n=0, lim, d = digits(2^n); if (#vecsort(d,,8) == #d, print1(n, ", ")););} \\ Michel Marcus, Aug 03 2015

a(n) = log_2(A260814(n)). - Zak Seidov, Aug 02 2015

A261315 Number of n-digit positive numbers whose digits occur with equal frequency.

Original entry on oeis.org

9, 90, 657, 4788, 27225, 146619, 544329, 2112084, 3447369, 28995255, 9, 1488185631, 9, 73556822205, 38222232057, 3321970172244, 9, 138479121435807, 9, 2209806802214163, 19711054740199689, 28570005, 9, 15574715941421647071, 141378216540777225, 421224309, 9724427617362202602009

Offset: 1

Robert Israel, Aug 14 2015

a(n) is divisible by 9.

a(n) = 9 if n > 10 is prime.

			For n = 1 there are the numbers 1 to 9.
For n = 2 there are 9 two-digit numbers of the form dd and 81 with two distinct digits, for a total of 90.
For n = 3 there are 9 numbers of the form ddd and 648 with three distinct digits, for a total of 657.
For n = 4 there are 9 numbers of the form dddd, 243 with two distinct digits each occurring twice, and 4536 with four distinct digits, for a total of 4788.

Robert Israel, Table of n, a(n) for n = 1..919

Cf. A052060.

seq(9/10*add(n!/(n/j)!^j * binomial(10,j), j = select(`<=`,numtheory:-divisors(n),10)),n=1..30);

a(n) = (9/10) * Sum_{j | n, j <= 10} n! * ((n/j)!)^(-j) * binomial(10,j).

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A045540 Numbers whose square contains an equal number of each digit that it contains.

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A084688 Nonnegative integers n such that 2^n uses only distinct decimal digits.

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A261315 Number of n-digit positive numbers whose digits occur with equal frequency.

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Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Formula