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A136836 Numbers k such that k and k^2 use only the digits 0, 1, 2 and 9. 3

%I #17 Feb 11 2024 12:25:32

%S 0,1,10,11,100,101,110,1000,1001,1010,1011,1100,1101,10000,10001,

%T 10010,10011,10100,10110,11000,11001,11010,100000,100001,100010,

%U 100011,100100,100101,100110,101000,101001,101100,110000,110001,110010,110100,1000000,1000001,1000010,1000011,1000100

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

%C Generated with DrScheme.

%C Comparison of b-files indicates that the first difference from A136831 is at the 1262nd entry. - _R. J. Mathar_ Apr 29 2008

%C 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

%H Jonathan Wellons, <a href="/A136836/b136836.txt">Table of n, a(n) for n = 1..1360</a>

%H J. Wellons, <a href="http://jonathanwellons.com/shared-digits/">Tables of Shared Digits</a>

%e 101090009991101^2 = 10219190120000900002099192201.

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

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

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

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

%K base,nonn

%O 1,3

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

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Last modified March 29 09:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)