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A277946 Squares whose largest decimal digit is 2.

%I A277946 #43 Nov 19 2024 22:11:46
%S A277946 121,10201,12100,22201,1002001,1020100,1022121,1210000,1212201,
%T A277946 2220100,100020001,100200100,100220121,102010000,102212100,121000000,
%U A277946 121022001,121220100,210221001,222010000,10000200001,10002000100,10002200121,10020010000,10020210201
%N A277946 Squares whose largest decimal digit is 2.
%C A277946 A subsequence of A000290.
%C A277946 From _Robert Israel_, Nov 14 2016: (Start)
%C A277946 If n is a term, then so is 100*n.
%C A277946 The first term with an even number of digits is a(36) = 100021020121.
%C A277946 The first term with an even number of digits that is not of the form a(36)*100^k has at least 24 digits.
%C A277946 (End)
%H A277946 Chai Wah Wu, <a href="/A277946/b277946.txt">Table of n, a(n) for n = 1..10000</a> (terms n = 1..50 from Colin Barker, terms n = 51..474 from Robert Israel)
%F A277946 a(n) = A277959(n)^2. Intersection of A000290 and A277964. - _M. F. Hasler_, Nov 15 2017
%p A277946 res:= NULL: B:= [1,2]:
%p A277946 for m from 1 to 10 do
%p A277946   for q in B do
%p A277946     for x from ceil(sqrt(10^m*q)) to floor(sqrt(10^m*q + 2/9*(10^m-1))) do
%p A277946       if max(convert(x^2,base,10)) = 2 then res:= res, x^2 fi
%p A277946   od od:
%p A277946   for q in B do
%p A277946      for x from ceil(sqrt(10^(m+1)*q)) to floor(sqrt(10^(m+1)*q + 2/9*(10^(m+1)-1))) do
%p A277946        if max(convert(x^2,base,10)) = 2 then res:= res, x^2 fi
%p A277946   od od:
%p A277946   if m < 10 then B:= map(t -> (10*t,10*t+1,10*t+2),B) fi;
%p A277946 od:
%p A277946 res; # _Robert Israel_, Nov 14 2016
%t A277946 fQ[n_] := Union[ IntegerDigits[ n^2]][[-1]] == 2; Select[ Range@100500, fQ]^2 (* _Robert G. Wilson v_, Nov 06 2016 *)
%o A277946 (PARI) L=List(); for(n=1, 10000, if(vecmax(digits(n^2))==2, listput(L, n^2))); Vec(L)
%o A277946 \\ See A277959 for more efficient code. - _M. F. Hasler_, Nov 16 2017
%o A277946 (Magma) [n^2: n in [1..1000000] | Maximum(Intseq(n^2)) eq 2]; // _Vincenzo Librandi_, Nov 06 2016
%Y A277946 Cf. A000290, A277947, A277948, A277959.
%K A277946 nonn,base
%O A277946 1,1
%A A277946 _Colin Barker_, Nov 05 2016