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

1,3

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

Links

Jonathan Wellons, Table of n, a(n) for n = 1..1360

J. Wellons, Tables of Shared Digits [archived]

Example

101090009991101^2 = 10219190120000900002099192201.

Mathematica

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

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.

Sequence in context: A278038 A136832 A136808 * A136827 A136831 A204009

Adjacent sequences: A136833 A136834 A136835 * A136837 A136838 A136839

Keyword

base,nonn

Author

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

Status

approved