A136836 Numbers k such that k and k^2 use only the digits 0, 1, 2 and 9.

0, 1, 10, 11, 100, 101, 110, 1000, 1001, 1010, 1011, 1100, 1101, 10000, 10001, 10010, 10011, 10100, 10110, 11000, 11001, 11010, 100000, 100001, 100010, 100011, 100100, 100101, 100110, 101000, 101001, 101100, 110000, 110001, 110010, 110100, 1000000, 1000001, 1000010, 1000011, 1000100

Offset: 1

Author

Jonathan Wellons (wellons(AT)gmail.com), Jan 22 2008

Keywords

• base
• nonn

Comments

Generated with DrScheme.

Comparison of b-files indicates that the first difference from A136831 is at the 1262nd entry. - R. J. Mathar Apr 29 2008

More precisely, A278038(18) = 10101, A136827(294) = 10110001101 resp. A136808(1262) = A136831(1262) = 101100000000000 are the first terms from where on these four sequences differ from the present one; a(1262) = 101090009991101 is also the first term containing a digit > 1. - M. F. Hasler, Nov 15 2017

Examples

			101090009991101^2 = 10219190120000900002099192201.
		

Links

• Jonathan Wellons, Table of n, a(n) for n = 1..1360
• J. Wellons, Tables of Shared Digits [archived]

Crossrefs

Cf. A136808, A136809, A136810, ..., A137147 for other digit combinations.

See also A058412 = A058411^2: squares having only digits {0,1,2}, A277946 = A277959^2 = squares whose largest digit is 2.

The first 1261 terms are also a subsequence of A278038 (binary numbers without '111'), in turn a subsequence of the binary numbers A007088.

Programs

Mathematica

With[{c={0,1,2,9}},Select[FromDigits/@Tuples[c,7],SubsetQ[c,IntegerDigits[#^2]]&]] (* Harvey P. Dale, Feb 11 2024 *)