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A181585 "Early bird" squares: write the square numbers in a string 149162536496481100... . Sequence gives numbers k such that k^2 occurs in the string ahead of its natural place.

%I A181585 #15 Jul 08 2021 11:45:12
%S A181585 7,8,21,25,46,97,129,161,196,221,245,258,277,296,350,436,460,592,661,
%T A181585 694,789,804,875,877,1250,2025,2221,3500,3959,4020,5461,5920,7925,
%U A181585 9607,12500,14772,19821,20010,21825,22011,22221,24012,25225,25375,25388,26013,28014
%N A181585 "Early bird" squares: write the square numbers in a string 149162536496481100... . Sequence gives numbers k such that k^2 occurs in the string ahead of its natural place.
%C A181585 Corresponding positions of the k^2's in a string 149162536496481100... are 2, 9, 23, 5, 112, 209, 395, 336, 496, 465, 656, 935, 65, 486, 603, 75, 112, 1115, 2317, 3163, 2329, 1987, 252, 421, 4036, 4279, 7092, ... .
%H A181585 Michael S. Branicky, <a href="/A181585/b181585.txt">Table of n, a(n) for n = 1..145</a>
%t A181585 s="1";ss={};Do[tsn=ToString[n^2];If[ !StringFreeQ[s,tsn],AppendTo[ss,n];Print[n]];s=s<>tsn,{n,2,99999}];
%o A181585 (Python)
%o A181585 def aupto(limit):
%o A181585     s, alst = "", []
%o A181585     for k in range(1, limit+1):
%o A181585         ss = str(k*k)
%o A181585         if ss in s: alst.append(k)
%o A181585         s += ss
%o A181585     return alst
%o A181585 print(aupto(28028)) # _Michael S. Branicky_, Jul 08 2021
%Y A181585 Cf. A000290, A116700, A141817.
%K A181585 base,nonn
%O A181585 1,1
%A A181585 _Zak Seidov_, Oct 31 2010
%E A181585 a(46) and beyond from _Michael S. Branicky_, Jul 08 2021