This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A175975 #33 Mar 22 2024 17:26:36
%S A175975 8,12,17,22,23,27,30
%N A175975 Numbers k with the property that k^k has exactly two 1's.
%C A175975 Next term (if any) > 10000. Is the sequence finite?
%C A175975 Any subsequent terms are > 10^5. - _Lucas A. Brown_, Mar 20 2024
%C A175975 From _David A. Corneth_, Mar 20 2024: (Start)
%C A175975 Any subsequent terms are > 10^9.
%C A175975 One could assume the digits to be random and look at the last few digits of k^k until it is clear that the number of 1's exceeds two. That way there is no need to compute k^k entirely.
%C A175975 Powers of 10 have exactly one digit 1 and so cannot be terms.
%C A175975 For 401113652 we have the last 253 digits containing exactly two 1's while the last 254 digits contain three 1's, proving that 401113652 is not a term. It appears that it usually takes the last 20 digits to prove that a number is not a term (the mode value); the median appears to be 27 digits. (End)
%e A175975 8^8 = 16777216,
%e A175975 12^12 = 8916100448256,
%e A175975 17^17 = 827240261886336764177,
%e A175975 22^22 = 341427877364219557396646723584,
%e A175975 23^23 = 20880467999847912034355032910567,
%e A175975 27^27 = 443426488243037769948249630619149892803,
%e A175975 30^30 = 205891132094649000000000000000000000000000000.
%t A175975 Select[Range[40],DigitCount[#^#,10,1]==2&] (* _Harvey P. Dale_, Dec 16 2013 *)
%o A175975 (Python)
%o A175975 A175975_list = [n for n in range(1000) if str(n**n).count('1') == 2] # _Chai Wah Wu_, May 19 2020
%Y A175975 Cf. A000312 (n^n), A043494.
%K A175975 nonn,base,more,less,hard
%O A175975 1,1
%A A175975 _Zak Seidov_, Nov 02 2010