

A272322


Numbers n such that n^n does not contain all ten decimal digits.


0



0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 27, 28, 30, 34, 40, 100, 1000, 10000, 100000, 1000000
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OFFSET

1,3


COMMENTS

A240963 is a subsequence.
A011557 is a subsequence. So this sequence is obviously infinite.
Conjecture: the only values > 40 are the powers of 10.  Franklin T. AdamsWatters, Apr 29 2016


LINKS

Table of n, a(n) for n=1..32.


EXAMPLE

27 is a term because 27^27 = 443426488243037769948249630619149892803 does not contain digit 5.
28 is a term because 28^28 = 33145523113253374862572728253364605812736 does not contain digit 9.


MATHEMATICA

{0}~Join~Select[Range[10^4], Times @@ DigitCount[#^#] == 0 &] (* Michael De Vlieger, Apr 25 2016 *)


PROG

(PARI) isA171102(n) = 9<#vecsort(Vecsmall(Str(n)), , 8);
lista(nn) = for(n=0, nn, if(!isA171102(n^n), print1(n, ", ")));
(PARI) is(n)=#Set(digits(n^n))<=9 \\ Charles R Greathouse IV, Apr 29 2016


CROSSREFS

Cf. A000312, A011557, A130696, A171102, A240963, A272269.
Sequence in context: A239427 A255422 A080681 * A246079 A246086 A194417
Adjacent sequences: A272319 A272320 A272321 * A272323 A272324 A272325


KEYWORD

nonn,base,more


AUTHOR

Altug Alkan, Apr 25 2016


EXTENSIONS

a(31) from Charles R Greathouse IV, Apr 29 2016
a(32) from Charles R Greathouse IV, May 03 2016


STATUS

approved



