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A100844 Smallest m greater than n such that m^2 contains n^2 in its decimal representation.

%I A100844 #20 Oct 04 2021 07:56:06
%S A100844 10,4,7,7,13,15,19,43,42,41,90,110,38,130,140,35,160,170,57,190,80,
%T A100844 210,220,227,240,75,260,223,279,196,70,219,320,330,340,285,360,370,
%U A100844 380,390,400,410,343,136,440,205,460,470,480,490,150,510,520,530,540,305,481
%N A100844 Smallest m greater than n such that m^2 contains n^2 in its decimal representation.
%C A100844 a(n) <= 10*n; a(A102576(n)) < 10*A102576(n), a(A102577(n)) = 10*A102577(n). - _Reinhard Zumkeller_, Jan 15 2005
%H A100844 Zak Seidov, <a href="/A100844/b100844.txt">Table of n, a(n) for n = 0..1000</a>
%e A100844 n=3: (3+1)^2 = 16, (3+2)^2 = 25 and (3+3)^2 = 36 do not contain 9 = 3^2, but 7^2 = 49 contains 9, therefore a(3) = 7.
%t A100844 p = -1; s = {}; m = 100; Do[p = p + 1; idp = IntegerDigits[p^2]; le = Length[idp]; q = p; Label[1]; q = q + 1; par = Partition[IntegerDigits[q^2], le, 1]; If[MemberQ[par, idp], AppendTo[s, q]; Goto[2], Goto[1]]; Label[2], {m}]; s (* _Zak Seidov_, Dec 19 2014 *)
%t A100844 f[n_] := Block[{sidn = ToString[n^2], k = n + 1}, While[ StringPosition[ ToString[k^2], sidn] == {}, k++]; k]; Array[f, 60, 0] (* _Robert G. Wilson v_, Dec 19 2014 *)
%o A100844 (Python)
%o A100844 def a(n):
%o A100844     s, m = str(n*n), n+1
%o A100844     while s not in str(m*m): m += 1
%o A100844     return m
%o A100844 print([a(n) for n in range(57)]) # _Michael S. Branicky_, Oct 04 2021
%Y A100844 Cf. A000290, A064735, A102576, A102577.
%K A100844 nonn,base
%O A100844 0,1
%A A100844 _Reinhard Zumkeller_, Jan 14 2005