A272322 Numbers n such that n^n does not contain all ten decimal digits.

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

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. Adams-Watters, 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: A255422 A080681 A366186 * A356800 A375590 A246079

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