A043494 -id:A043494 - cp's OEIS frontend

A111066 Numbers with digits 1 and 2 and at least one of each.

12, 21, 112, 121, 122, 211, 212, 221, 1112, 1121, 1122, 1211, 1212, 1221, 1222, 2111, 2112, 2121, 2122, 2211, 2212, 2221, 11112, 11121, 11122, 11211, 11212, 11221, 11222, 12111, 12112, 12121, 12122, 12211, 12212, 12221, 12222, 21111, 21112, 21121, 21122, 21211

Offset: 1

Alexandre Wajnberg & Youri Mora, Oct 08 2005

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Equals A007931 minus A000042 and A002276. Supersequence of A214218.

Cf. A043494, A037415, A062289, A000225.

FromDigits /@ Select[ IntegerDigits[ Range[210], 3], Union[ # ] == {1, 2} &] (* Robert G. Wilson v, Oct 09 2005 *)
Union[FromDigits/@Select[Flatten[Table[Tuples[{1,2},n],{n,2,5}],1], Union[#] == {1,2}&]] (* Harvey P. Dale, Sep 05 2013 *)

from itertools import count, islice
def agen():
    for i in count(1):
        s = bin(i+1)[3:].replace('1', '2').replace('0', '1')
        if 0 < s.count('1') < len(s):
            yield int(s)
print(list(islice(agen(), 42))) # Michael S. Branicky, Dec 21 2021

More terms from Robert G. Wilson v, Oct 09 2005

Crossrefs from Charles R Greathouse IV, Aug 03 2010

A175975 Numbers k with the property that k^k has exactly two 1's.

Original entry on oeis.org

8, 12, 17, 22, 23, 27, 30

Offset: 1

Zak Seidov, Nov 02 2010

Next term (if any) > 10000. Is the sequence finite?
Any subsequent terms are > 10^5. - Lucas A. Brown, Mar 20 2024
From David A. Corneth, Mar 20 2024: (Start)
Any subsequent terms are > 10^9.
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.
Powers of 10 have exactly one digit 1 and so cannot be terms.
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)

			8^8 = 16777216,
12^12 = 8916100448256,
17^17 = 827240261886336764177,
22^22 = 341427877364219557396646723584,
23^23 = 20880467999847912034355032910567,
27^27 = 443426488243037769948249630619149892803,
30^30 = 205891132094649000000000000000000000000000000.

Cf. A000312 (n^n), A043494.

Select[Range[40],DigitCount[#^#,10,1]==2&] (* Harvey P. Dale, Dec 16 2013 *)

A175975_list = [n for n in range(1000) if str(n**n).count('1') == 2] # Chai Wah Wu, May 19 2020

cp's OEIS Frontend

A111066 Numbers with digits 1 and 2 and at least one of each.

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