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A154532 a(n) = largest 10-digit number whose n-th power contains each digit (0-9) n times 7
9876543210, 9994363488, 9999257781, 9999112926, 9995722269, 9999409158, 9998033316, 9993870774, 9986053188, 9964052493, 9975246786, 9966918135, 9938689137, 9998781633, 9813743148, 9970902252, 9740383767, 9829440591 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A number with 10*n digits may have all ten digits(0-9) repeated n times. The probability of this is (10n)!/((n!)^10 * 10^((10*n)-10^(10*n-1)). There are 10^10-10^(10-1/n)) numbers which are n-th powers of some 10-digit numbers. So there may exist Count=(10n)!*(10^10-10^(10-1/n)))/((n!)^10 * 10^((10*n)-10^(2*n-1)) numbers with the desired property.

LINKS

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

Zhining Yang, Largest Ten Digit Powers

EXAMPLE

For n=18,a(n)=9829440591. That means 9829440591^18 has all digit(0-9) each for 18 times.

PROG

(Other) VB code:

Function befit(ByVal s As String, ByVal num As Long) As Boolean 'tell if a string s contain all digit(0-9) for just num times Dim b(9) As Long, t As Long befit = True 'init If Len(s) <> 10 * num Then befit = False: Exit

Function For i = 1 To Len(s) t = Val(Mid(s, i, 1)) b(t) = b(t) + 1 If b(t) > num Then befit = False: Exit Function Next End Function

Function mypower(ByVal num As Currency, ByVal power As Long) As String 'UDF to calculate powers of a 10-digit number Dim b(), temp ReDim b(1 To 2 * power) ReDim s(1 To 2 * power) 'The last two element of the result, i.e. num it self b(2 * power - 1) = Val(Left(num, 5)) 'init b(2 * power) = Val(Right(num, 5)) 'init For i = 2 To power temp = 0 For j = 2 * power To 1 Step -1 temp = b(j) * num + temp b(j) = Format(Val(Right(temp, 5)), "00000") '100000 adic temp = Int(temp / 10 ^ 5) Next Next mypower = Join(b, "") 'The final result End Function

Private Sub Command1_Click() Dim index As Long, j As Currency, s As String For index = 2 To 20 For j = 9999999999# To Int(10 ^ (10 - 1 / index)) + 1 Step -3 'n times 0-9 must be divisible by 3 DoEvents s = mypower(j, index) 'the result If befit(s, index) Then 's contains 0-9 each for index times Open "c:\9876543210.txt" For Append As #1 'Output to a text file Print #1, j & "^" & index & "=" & s 'Print the result Close #1 End If Exit For 'Loop for next index Next End End Sub

CROSSREFS

Cf. A010784 A078255

Sequence in context: A204058 A328291 A328292 * A157745 A159473 A174844

Adjacent sequences:  A154529 A154530 A154531 * A154533 A154534 A154535

KEYWORD

nonn,base

AUTHOR

Zhining Yang, Jan 11 2009

EXTENSIONS

Edited by N. J. A. Sloane, Jan 12 2008

STATUS

approved

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Last modified July 31 02:33 EDT 2021. Contains 346367 sequences. (Running on oeis4.)