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When squared gives number composed of digits {1,2,3}.
9

%I #21 Aug 11 2024 14:41:30

%S 1,11,111,36361,363639,461761,3636361,34815389,362397739,176412364139,

%T 57637950363639,3497458093147239,56843832676142723489,

%U 557963558954625926861

%N When squared gives number composed of digits {1,2,3}.

%H P. De Geest, <a href="https://www.worldofnumbers.com/threedigits.htm">Squares containing at most three distinct digits, Index entries for related sequences</a>

%H Author?, <a href="http://web.archive.org/web/20080517071411/http://web.archive.org/web/20080708203024/http://blue.kakiko.com/mmrmmr/htm/eqtn06.html">Source</a>(<a href="http://web.archive.org/web/20060426155831/http://web.archive.org/web/20060426155831/http://blue.kakiko.com/mmrmmr/txt/eqtn06.txt">txt</a>)

%H Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/math02/math0210.htm">Sporadic tridigital solutions</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SquareNumber.html">Square Number.</a>

%H <a href="/index/Sq#squares">Index entries for sequences related to squares</a>.

%F a(n)^2 = A030174(n). - _M. F. Hasler_, Nov 16 2017

%t Do[ If[ Union[ Join[{1, 2, 3}, IntegerDigits[n^2] ] ] == {1, 2, 3}, Print[n] ], {n, 0, 10^9}]

%o (PARI) lista(nn) = for(n=1, nn, if(setminus(vecsort(digits(n^2), , 8), [1, 2, 3])==[], print1(n, ", "))) \\ _Iain Fox_, Nov 16 2017

%Y Cf. A030174; A000290.

%Y Cf. A006716 = A027675^2, A030176 = A030177^2, A058411^2 = A058412, ..., A058473^2 = A058474.

%Y Cf. A136808, A136809, ..., A137147: n and n^2 have digits {...}.

%Y Cf. A277959^2 = A277946 and A277960^2 = A277947: squares whose largest digit is 2 resp. 3.

%K nonn,base

%O 1,2

%A _Patrick De Geest_

%E More terms from _Patrick De Geest_, Mar 01 2000

%E More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 14 2005

%E Offset corrected by _Iain Fox_, Nov 16 2017