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

Author

Altug Alkan, Apr 25 2016

Keywords

• nonn
• base
• more

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

Examples

			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.
		

Crossrefs

Cf. A000312, A011557, A130696, A171102, A240963, A272269.

Programs

Mathematica

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

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

Extensions

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

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