login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A062518 Conjectural largest exponent k such that n^k does not possess all of the digits 0 through 9 (in decimal notation) or 0 if no such k exists (if n is a power of 10). 3
0, 168, 106, 84, 65, 64, 61, 56, 53, 0, 41, 51, 37, 34, 34, 42, 27, 25, 44, 168, 29, 24, 50, 23, 29, 31, 28, 28, 45, 106, 28, 18, 24, 34, 18, 32, 25, 17, 41, 84, 23, 19, 20, 29, 39, 32, 15, 29, 16, 65, 29, 29, 30, 18, 17, 33, 19, 31, 27, 64, 26, 19, 24, 28, 17, 15, 21, 25, 13 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

I do not know how many of these terms have been proved to be correct - N. J. A. Sloane.

In particular, are the powers of 10 the only n with a(n) = 0?

Note that a(10n) = a(n) unless n^a(n) contains no 0 (i.e. a(n) = A020665(n)), in which case a(10n) < a(n). - Christopher J. Smyth, Aug 20 2014

LINKS

Table of n, a(n) for n=1..69.

EXAMPLE

a(11) = 41 as 11^41 = 4978518112499354698647829163838661251242411 is the conjectural highest power of 11 not containing all ten digits.

a(110) = 38 as 110^38 does not contain the digit 2, while, conjecturally, all higher powers of 110 contain all ten digits. - Christopher J. Smyth, Aug 20 2014

MATHEMATICA

Do[ If[ IntegerQ[ Log[10, n] ], Print[0], Print[ Select[ Range[25000], Union[ IntegerDigits[n^# ] ] != {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} &] [[ -1]] ] ], {n, 1, 100} ]

CROSSREFS

Cf. A090493, A020665.

Sequence in context: A289743 A308280 A259086 * A038823 A296890 A225535

Adjacent sequences:  A062515 A062516 A062517 * A062519 A062520 A062521

KEYWORD

base,nonn

AUTHOR

Robert G. Wilson v, Jun 24 2001

EXTENSIONS

Definition corrected by Christopher J. Smyth, Aug 20 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 14 19:48 EDT 2020. Contains 335729 sequences. (Running on oeis4.)