

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
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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



